ORXOR-four studies together

1 Study 1: In-lab ORXOR

2 Study 2: Online ORXOR

df.total.valid.2 <- read.csv('../Data/Study1/online/Study1b_1.csv')
df.rating.2 <- read.csv('../Data/Study1/online/Study1b_2.csv')

df.rating.2.summary <- df.rating.2 %>% group_by(participant) %>%
  summarise(medianValue=median(value),
            avgValue=mean(value)) %>% ungroup()

3 Study 3: Online ORXOR-D

df.total.valid.3 <- read.csv('../Data/Study2/Study2_1.csv')
df.rating.3 <- read.csv('../Data/Study2/Study2_2.csv')

df.rating.3.summary <- df.rating.3 %>% group_by(participant) %>%
  summarise(medianValue=median(value),
            avgValue=mean(value)) %>% ungroup()

4 Apply exclusion criteria

Study 2 and 3: matched with study 1 regarding the likelihood of opposite actions

df.total.rt.12 <- rbind(df.total.rt.1 %>% dplyr::select(-sex) %>% mutate(study='S1',
                                                                  participant=as.character(participant)),
                        df.total.rt.2 %>% mutate(study='S2')) %>%
  dplyr::mutate(scaledMeanValue=scale(meanValue),
                scaledValueDiff=scale(valueDiff),
                scaledTrialNum=scale(trialN),
                catChoiceCondition=relevel(factor(catChoiceCondition),ref='XOR'),
                acc=as.factor(isBestFirst==1))
df.total.valid.12 <- rbind(df.total.valid.1 %>% dplyr::select(-sex) %>% mutate(study='S1',
                                                                        participant=as.character(participant)),
                           df.total.valid.2 %>% mutate(study='S2')) %>% mutate(study=factor(study)) %>%
  dplyr::mutate(scaledMeanValue=scale(meanValue),
                scaledValueDiff=scale(valueDiff),
                scaledTrialNum=scale(trialN),
                catChoiceCondition=relevel(factor(catChoiceCondition),ref='XOR'))
contrasts(df.total.rt.12$catChoiceCondition)<-contr.sdif
contrasts(df.total.rt.12$acc)<-contr.sdif
contrasts(df.total.valid.12$catChoiceCondition)<-contr.sdif

4.1 Selection Task - Models

model.RT.12 <- lmerTest::lmer(firstRT ~ catChoiceCondition * scaledMeanValue + catChoiceCondition * scaledValueDiff + scaledTrialNum + 
                     (1 + catChoiceCondition * scaledMeanValue + catChoiceCondition * scaledValueDiff + scaledTrialNum|participant),
                   data=df.total.rt.12)

## boundary (singular) fit: see help('isSingular')

anova(model.RT.12)

## Type III Analysis of Variance Table with Satterthwaite's method
##                                     Sum Sq Mean Sq NumDF   DenDF F value
## catChoiceCondition                  48.243  48.243     1  79.065  53.621
## scaledMeanValue                    203.049 203.049     1  62.011 225.686
## scaledValueDiff                    129.075 129.075     1  64.569 143.464
## scaledTrialNum                      27.156  27.156     1  78.985  30.184
## catChoiceCondition:scaledMeanValue  20.675  20.675     1  64.490  22.980
## catChoiceCondition:scaledValueDiff   0.167   0.167     1 134.058   0.186
##                                       Pr(>F)    
## catChoiceCondition                 1.788e-10 ***
## scaledMeanValue                    < 2.2e-16 ***
## scaledValueDiff                    < 2.2e-16 ***
## scaledTrialNum                     4.646e-07 ***
## catChoiceCondition:scaledMeanValue 1.002e-05 ***
## catChoiceCondition:scaledValueDiff    0.6669    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

model.acc.12 <- glmer(isBestFirst ~ catChoiceCondition * scaledMeanValue + catChoiceCondition * scaledValueDiff +
                        scaledTrialNum + 
                     (1 + catChoiceCondition * scaledMeanValue + catChoiceCondition * scaledValueDiff +
                        scaledTrialNum|participant),
                     data=df.total.rt.12,family=binomial,control = glmerControl(optCtrl = list(maxfun=20000)))

## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 0.00987731 (tol = 0.002, component 1)

anova(model.acc.12)

## Analysis of Variance Table
##                                    npar  Sum Sq Mean Sq  F value
## catChoiceCondition                    1   3.538   3.538   3.5377
## scaledMeanValue                       1   0.033   0.033   0.0328
## scaledValueDiff                       1 301.164 301.164 301.1639
## scaledTrialNum                        1   1.803   1.803   1.8033
## catChoiceCondition:scaledMeanValue    1   1.365   1.365   1.3655
## catChoiceCondition:scaledValueDiff    1   1.404   1.404   1.4041

tab_model(model.RT.12,model.acc.12,transform = NULL,show.re.var = F,pred.labels = c("Intercept","Inclusivity","Overall Value","Relative Value","Trial Order","Incl by OV","Incl by RV"),dv.labels = c("RT","Accuracy"))

	RT			Accuracy
Predictors	Estimates	CI	p	Log-Odds	CI	p
Intercept	2.72	2.56 – 2.88	<0.001	-0.09	-0.19 – 0.01	0.083
Inclusivity	-0.30	-0.38 – -0.22	<0.001	-0.10	-0.19 – -0.01	0.029
Overall Value	-0.36	-0.41 – -0.31	<0.001	0.01	-0.06 – 0.08	0.790
Relative Value	-0.19	-0.22 – -0.16	<0.001	0.65	0.57 – 0.73	<0.001
Trial Order	-0.12	-0.16 – -0.08	<0.001	-0.03	-0.08 – 0.01	0.164
Incl by OV	-0.14	-0.20 – -0.08	<0.001	-0.08	-0.19 – 0.03	0.148
Incl by RV	0.01	-0.04 – 0.06	0.666	-0.06	-0.17 – 0.04	0.246
ICC				0.08
N	82 participant			82 participant
Observations	10138			10138
Marginal R2 / Conditional R2	0.158 / NA			0.105 / 0.178

model.acc.12.dummy <- lmer(isBestFirst ~ catChoiceCondition * scaledMeanValue + catChoiceCondition * scaledValueDiff +
                        scaledTrialNum + 
                     (1 + catChoiceCondition * scaledMeanValue + catChoiceCondition * scaledValueDiff +
                        scaledTrialNum|participant),
                     data=df.total.rt.12,control = lmerControl(optCtrl = list(maxfun=20000)))

## boundary (singular) fit: see help('isSingular')

model.RT.12.coeff <- lmerTest::lmer(firstRT ~ catChoiceCondition / scaledMeanValue + catChoiceCondition / scaledValueDiff + scaledTrialNum + (1 + catChoiceCondition / scaledMeanValue + catChoiceCondition / scaledValueDiff + scaledTrialNum|participant), 
                   data=df.total.rt.12,
                   control=lmerControl(optCtrl=list(maxfun=1e6)))

## boundary (singular) fit: see help('isSingular')

model.acc.12.coeff <- glmer(isBestFirst ~ catChoiceCondition / scaledMeanValue + catChoiceCondition / scaledValueDiff + scaledTrialNum + 
                     (1 + catChoiceCondition / scaledMeanValue + catChoiceCondition / scaledValueDiff + scaledTrialNum|participant),
                     data=df.total.rt.12,family=binomial)

## boundary (singular) fit: see help('isSingular')

df.total.rt.12.rr <- df.total.rt.12 %>% mutate(rr=firstValue/firstRT) 


model.rr.12 <- lmerTest::lmer(rr ~ catChoiceCondition * (scaledMeanValue + scaledValueDiff) + scaledTrialNum + 
                     (1 + catChoiceCondition * (scaledMeanValue + scaledValueDiff) + scaledTrialNum|participant),
                   data=df.total.rt.12.rr,
                   control=lmerControl(optCtrl=list(maxfun=1e6)))

## boundary (singular) fit: see help('isSingular')

## Warning: Model failed to converge with 1 negative eigenvalue: -4.2e+02

tab_model(model.rr.12,dv.labels = c('Reward Rate'),pred.labels = c('Intercept','OR - XOR','Mean Value','Value Diff','Trial Num','Incl X Mean Value','Incl X Value Diff'))

	Reward Rate
Predictors	Estimates	CI	p
Intercept	3.31	2.98 – 3.63	<0.001
OR - XOR	0.36	0.24 – 0.48	<0.001
Mean Value	1.34	1.20 – 1.48	<0.001
Value Diff	0.44	0.37 – 0.50	<0.001
Trial Num	0.12	0.01 – 0.23	0.033
Incl X Mean Value	0.26	0.16 – 0.36	<0.001
Incl X Value Diff	0.02	-0.07 – 0.10	0.720
Random Effects
σ2	3.51
τ00 participant	2.20
τ11 participant.catChoiceConditionOR-XOR	0.19
τ11 participant.scaledMeanValue	0.38
τ11 participant.scaledValueDiff	0.04
τ11 participant.scaledTrialNum	0.23
τ11 participant.catChoiceConditionOR-XOR:scaledMeanValue	0.07
τ11 participant.catChoiceConditionOR-XOR:scaledValueDiff	0.00
ρ01	-0.04
	1.00
	-0.79
	-0.10
	0.14
	0.18
N participant	82
Observations	10138
Marginal R2 / Conditional R2	0.329 / NA

model.conflict.12 <- lmerTest::lmer(conflict ~ catChoiceCondition * poly(scaledMeanValue,2) + catChoiceCondition * scaledValueDiff + scaledTrialNum + (1 + catChoiceCondition * poly(scaledMeanValue,2) + catChoiceCondition * scaledValueDiff + scaledTrialNum|participant),data=df.total.valid.12)

## boundary (singular) fit: see help('isSingular')

## Warning: Model failed to converge with 2 negative eigenvalues: -9.2e-04
## -3.8e-03

tab_model(model.conflict.12,transform = NULL,show.re.var = F,pred.labels = c("Intercept","Inclusivity","Overall Value","Overall Value^2","Relative Value","Trial Order","Incl by OV","Incl by OV^2","Incl by RV"),dv.labels = c("Conflict"))

	Conflict
Predictors	Estimates	CI	p
Intercept	2.39	2.25 – 2.52	<0.001
Inclusivity	-0.46	-0.62 – -0.30	<0.001
Overall Value	15.18	4.64 – 25.72	0.005
Overall Value^2	12.79	8.11 – 17.46	<0.001
Relative Value	-0.07	-0.10 – -0.03	<0.001
Trial Order	0.01	-0.03 – 0.05	0.723
Incl by OV	-18.83	-27.12 – -10.53	<0.001
Incl by OV^2	-4.70	-9.79 – 0.39	0.070
Incl by RV	0.00	-0.04 – 0.05	0.910
N participant	82
Observations	10520
Marginal R2 / Conditional R2	0.124 / NA

df.total.rt.12$scaledRT<-scale(df.total.rt.12$firstRT)

model.conflict.12.rt <- lmerTest::lmer(conflict ~ scaledRT + acc + catChoiceCondition * poly(scaledMeanValue,2) + catChoiceCondition * scaledValueDiff + scaledTrialNum + (1 + scaledRT + acc + catChoiceCondition * poly(scaledMeanValue,2) + catChoiceCondition * scaledValueDiff + scaledTrialNum|participant),data=df.total.rt.12)

## boundary (singular) fit: see help('isSingular')

## Warning: Model failed to converge with 2 negative eigenvalues: -1.8e-03
## -2.0e-02

tab_model(model.conflict.12.rt,transform = NULL,show.re.var = F,pred.labels = c("Intercept","RT","Accuracy","Inclusivity","Overall Value","Overall Value^2","Relative Value","Trial Order","Incl by OV","Incl by OV^2","Incl by RV"),dv.labels = c("Conflict"))

	Conflict
Predictors	Estimates	CI	p
Intercept	2.36	2.23 – 2.50	<0.001
RT	0.09	0.05 – 0.13	<0.001
Accuracy	-0.09	-0.13 – -0.05	<0.001
Inclusivity	-0.44	-0.60 – -0.28	<0.001
Overall Value	19.45	10.14 – 28.77	<0.001
Overall Value^2	10.94	6.37 – 15.50	<0.001
Relative Value	-0.03	-0.06 – 0.00	0.069
Trial Order	0.01	-0.03 – 0.05	0.714
Incl by OV	-17.46	-25.30 – -9.62	<0.001
Incl by OV^2	-5.06	-10.08 – -0.04	0.048
Incl by RV	-0.01	-0.06 – 0.04	0.822
N participant	82
Observations	10138
Marginal R2 / Conditional R2	0.132 / NA

df.total.valid.12.lvd <- df.total.valid.12 %>% filter(valueDiff<1) %>%
  mutate(scaledMeanValue=scale(meanValue),
         scaledValueDiff=scale(valueDiff),
         scaledTrialNum=scale(trialN))


model.conflict.12.lvd <- lmerTest::lmer(conflict ~ catChoiceCondition * poly(scaledMeanValue,2) + catChoiceCondition * scaledValueDiff + scaledTrialNum + (1 + catChoiceCondition * poly(scaledMeanValue,2) + catChoiceCondition * scaledValueDiff + scaledTrialNum|participant),data=df.total.valid.12.lvd)

## boundary (singular) fit: see help('isSingular')

## Warning: Model failed to converge with 1 negative eigenvalue: -3.5e-05

tab_model(model.conflict.12.lvd,transform = NULL,show.re.var = F,pred.labels = c("Intercept","Inclusivity","Overall Value","Overall Value^2","Relative Value","Trial Order","Incl by OV","Incl by OV^2","Incl by RV"),dv.labels = c("Conflict"))

	Conflict
Predictors	Estimates	CI	p
Intercept	2.54	2.40 – 2.68	<0.001
Inclusivity	-0.45	-0.64 – -0.25	<0.001
Overall Value	11.22	5.02 – 17.41	<0.001
Overall Value^2	9.17	5.20 – 13.13	<0.001
Relative Value	-0.01	-0.06 – 0.03	0.521
Trial Order	-0.01	-0.06 – 0.04	0.619
Incl by OV	-7.62	-14.12 – -1.12	0.022
Incl by OV^2	-1.80	-7.37 – 3.76	0.525
Incl by RV	0.10	0.02 – 0.18	0.019
N participant	82
Observations	2638
Marginal R2 / Conditional R2	0.154 / NA

p1 <- ggplot(df.total.rt.12 %>% filter(catChoiceCondition=='XOR'), aes(meanValue,valueDiff)) + geom_point(color='#0673C3',size=0.5) + theme_classic() + xlab('Overall value') + ylab('Relative Value') + theme(legend.justification=c(1,1),legend.position='none',text = element_text(size=6),strip.text.y = element_blank())
p1 <- ggExtra::ggMarginal(p1, type = "histogram") 

p2 <- ggplot(df.total.rt.12 %>% filter(catChoiceCondition=='OR'), aes(meanValue,valueDiff)) + geom_point(color='#00B024',size=0.5) + theme_classic() +  xlab('Overall value') + ylab('Relative Value') + theme(legend.justification=c(1,1),legend.position='none',text = element_text(size=6),strip.text.y = element_blank())
p2 <- ggExtra::ggMarginal(p2, type = "histogram") 

ggsave(filename = '../Figures/Figure_MVDV1.pdf',p1,units = 'cm',width = 3,height = 3)
ggsave(filename = '../Figures/Figure_MVDV2.pdf',p2,units = 'cm',width = 3,height = 3)

eff_mv.cfl.12 <- Effect(c("scaledMeanValue","catChoiceCondition"),
                   model.conflict.12.lvd,
                   xlevels=list(scaledMeanValue=seq(quantile(df.total.valid.12$scaledMeanValue,0.025),
                                                    quantile(df.total.valid.12$scaledMeanValue,0.975),0.1)))

## Warning in Analyze.model(focal.predictors, mod, xlevels, default.levels, : the
## predictors scaledValueDiff, scaledTrialNum, scaledMeanValue are one-column
## matrices that were converted to vectors

IA.mv.cfl.12 <- as.data.frame(eff_mv.cfl.12)

IA.mv.cfl.12$catChoiceCondition <- relevel(IA.mv.cfl.12$catChoiceCondition,ref = 'XOR')

p.eff.mv.cfl.12<-ggplot(data=IA.mv.cfl.12, aes(x=scaledMeanValue, y=fit,group=catChoiceCondition)) + 
  geom_line(size=0.5,aes(color=catChoiceCondition))+theme_bw(12) +
  geom_ribbon(data=IA.mv.cfl.12, aes(x=scaledMeanValue, max = upper, min = lower,fill=catChoiceCondition),alpha=0.3, inherit.aes = FALSE)+ 
  xlab("Overall value\n(z-scored)") + ylab("Conflict") + 
  theme(panel.border = element_blank(), panel.grid.major = element_blank(), plot.title = element_text(hjust = 0.5,size=6),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black")) +
  theme(legend.justification=c(1,1),legend.position='none',text = element_text(size=6),strip.text.y = element_blank()) + 
  scale_fill_manual("",values=c('#0673C3','#00B024','#008012')) + 
  scale_color_manual("",values=c('#0673C3','#00B024','#008012')) + 
  coord_cartesian(ylim=c(1,5)) + scale_y_continuous(breaks = c(1,5))

## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.

ggsave(filename = '../Figures/Figure_LVD.pdf',p.eff.mv.cfl.12,units = 'cm',width = 3,height = 3)

df.volun.summary <- df.total.rt.12 %>% filter(catChoiceCondition=='OR',NChosen >= 1) %>% 
  rowwise() %>% dplyr::mutate(totalRT=getSumRT(c(RT1,RT2,RT3,RT4),
                                        c(Order1,Order2,Order3,Order4))) %>% ungroup() %>%
  group_by(NChosen) %>% summarise(ntrial=n(),
                                  meanSumRT=mean(totalRT))

df.volun.RT.summary.1 <- df.total.rt.12 %>% filter(catChoiceCondition=='OR',firstRT>0) %>% group_by(NChosen) %>%
  summarise(sRT=mean(firstRT)) %>% mutate(selection = 1)

df.volun.RT.summary.2 <- df.total.rt.12 %>% rowwise() %>% mutate(secondRT=getSecond(c(RT1,RT2,RT3,RT4),
                                        c(Order1,Order2,Order3,Order4))) %>% ungroup() %>% filter(catChoiceCondition=='OR',secondRT>0) %>% group_by(NChosen) %>%
  summarise(sRT=mean(secondRT-firstRT)) %>% mutate(selection = 2)

df.volun.RT.summary.3 <- df.total.rt.12 %>% 
  rowwise() %>% dplyr::mutate(secondRT=getSecond(c(RT1,RT2,RT3,RT4),
                                        c(Order1,Order2,Order3,Order4)),thirdRT=getThird(c(RT1,RT2,RT3,RT4),
                                        c(Order1,Order2,Order3,Order4))) %>% ungroup() %>% filter(catChoiceCondition=='OR',thirdRT>0) %>%  group_by(NChosen) %>%
  summarise(sRT=mean(thirdRT-secondRT)) %>% mutate(selection = 3)

df.volun.RT.summary.4 <- df.total.rt.12 %>% 
  rowwise() %>% dplyr::mutate(fourthRT=getFourth(c(RT1,RT2,RT3,RT4),
                                        c(Order1,Order2,Order3,Order4)),
                              thirdRT=getThird(c(RT1,RT2,RT3,RT4),
                                        c(Order1,Order2,Order3,Order4))) %>% ungroup() %>% filter(catChoiceCondition=='OR',fourthRT>0) %>%  group_by(NChosen) %>%
  summarise(sRT=mean(fourthRT-thirdRT)) %>% mutate(selection = 4)

df.volun.RT.summary <- inner_join(rbind(df.volun.RT.summary.1,df.volun.RT.summary.2,
                             df.volun.RT.summary.3,df.volun.RT.summary.4) %>%  pivot_wider(
    names_from = selection,
    values_from = sRT,names_prefix='sRT_'
  ),df.volun.summary,by='NChosen')

coeff.rt <- t(fixef(model.RT.12)['catChoiceConditionOR-XOR'])
df.ci <- confint(model.RT.12,method="Wald")
df.ci <- df.ci[!is.na(df.ci[,1]),]
ci.rt <- df.ci['catChoiceConditionOR-XOR',]
estimate.rt <- cbind(coeff.rt,t(ci.rt))
colnames(estimate.rt)<-c('coeff','lower','upper')

coeff.acc <- t(fixef(model.acc.12.dummy)['catChoiceConditionOR-XOR'])
df.ci <- confint(model.acc.12.dummy,method="Wald")
df.ci <- df.ci[!is.na(df.ci[,1]),]
ci.acc <- df.ci['catChoiceConditionOR-XOR',]
estimate.acc <- cbind(coeff.acc,t(ci.acc))
colnames(estimate.acc)<-c('coeff','lower','upper')

coeff.conf <- t(fixef(model.conflict.12)['catChoiceConditionOR-XOR'])
df.ci <- confint(model.conflict.12,method="Wald")
df.ci <- df.ci[!is.na(df.ci[,1]),]
ci.conf <- df.ci['catChoiceConditionOR-XOR',]
estimate.conf <- cbind(coeff.conf,t(ci.conf))
colnames(estimate.conf)<-c('coeff','lower','upper')

coeff.rr <- t(fixef(model.rr.12)['catChoiceConditionOR-XOR'])
df.ci <- confint(model.rr.12,method="Wald")
df.ci <- df.ci[!is.na(df.ci[,1]),]
ci.rr <- df.ci['catChoiceConditionOR-XOR',]
estimate.rr <- cbind(coeff.rr,t(ci.rr))
colnames(estimate.rr)<-c('coeff','lower','upper')

estimate.all <- data.frame(rbind(estimate.rt,estimate.acc,estimate.conf,estimate.rr))
estimate.all$var <- c('RT','Acc','Conflict','RR')

p.diff.acc.12 <- ggplot(estimate.all %>% filter(var %in% c('Acc')), aes(x=var, y=coeff))  + geom_hline(yintercept=0,color='#555555',size=0.2) + 
  geom_point(stat="identity", position=position_dodge(0.6),size=0.5) +
  geom_errorbar(aes(ymin=lower, ymax=upper), width=0.1,size=0.4,
                 position=position_dodge(.6))+labs(x="", y = "Effect of Inclusivity")+theme_bw(12) + 
  theme(panel.border = element_blank(),panel.grid.major = element_blank(),
        axis.title.x = element_text(margin = margin(t = 0, r = 0, b = 0, l = 0)),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),axis.ticks =element_line(size=0.2),
        text=element_text(size=6),legend.position="none") +
  scale_x_discrete(labels=c("Acc"='P(Best First)')) + scale_y_continuous(limits = c(-0.1,0.004),breaks = c(-0.1,0))

## Warning: The `size` argument of `element_line()` is deprecated as of ggplot2 3.4.0.
## ℹ Please use the `linewidth` argument instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.

p.diff.acc.12

p.diff.rt.12 <- ggplot(estimate.all %>% filter(var %in% c('RT')), aes(x=var, y=coeff))  + geom_hline(yintercept=0,color='#555555',size=0.2) + 
  geom_point(stat="identity", position=position_dodge(0.6),size=0.5) +
  geom_errorbar(aes(ymin=lower, ymax=upper), width=0.1,size=0.4,
                 position=position_dodge(.6))+labs(x="", y = "Effect of Inclusivity\n(sec)")+theme_bw(12) + 
  theme(panel.border = element_blank(),panel.grid.major = element_blank(),
        axis.title.x = element_text(margin = margin(t = 0, r = 0, b = 0, l = 0)),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),axis.ticks =element_line(size=0.2),
        text=element_text(size=6),legend.position="none") +
  scale_x_discrete(labels=c("RT"='RT')) + scale_y_continuous(limits = c(-0.5,0.02),breaks = c(-0.5,0))

p.diff.rt.12

p.diff.conflict.12 <- ggplot(estimate.all %>% filter(var %in% c('Conflict')), aes(x=var, y=coeff))  + geom_hline(yintercept=0,color='#555555',size=0.2) + 
  geom_point(stat="identity", position=position_dodge(0.6),size=0.5) +
  geom_errorbar(aes(ymin=lower, ymax=upper), width=0.1,size=0.4,
                 position=position_dodge(.6))+labs(x="", y = "Effect of Inclusivity")+theme_bw(12) + 
  theme(panel.border = element_blank(),panel.grid.major = element_blank(),
        axis.title.x = element_text(margin = margin(t = 0, r = 0, b = 0, l = 0)),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),axis.ticks =element_line(size=0.2),
        text=element_text(size=6),legend.position="none") +
  scale_x_discrete(labels=c("Conflict"='Conflict')) + scale_y_continuous(limits = c(-1,.02),breaks = c(-1,0))
p.diff.conflict.12

p.diff.rr.12 <- ggplot(estimate.all %>% filter(var %in% c('RR')), aes(x=var, y=coeff))  + geom_hline(yintercept=0,color='#555555',size=0.2) + 
  geom_point(stat="identity", position=position_dodge(0.6),size=0.5) +
  geom_errorbar(aes(ymin=lower, ymax=upper), width=0.1,size=0.4,
                 position=position_dodge(.6))+labs(x="", y = "Effect of Inclusivity\n(Unit Value/sec)")+theme_bw(12) + 
  theme(panel.border = element_blank(),panel.grid.major = element_blank(),
        axis.title.x = element_text(margin = margin(t = 0, r = 0, b = 0, l = 0)),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),
        text=element_text(size=6),legend.position="none",axis.ticks =element_line(size=0.2)) +
  scale_x_discrete(labels=c("RR"='Reward Rate')) + scale_y_continuous(limits = c(-0.02,0.5),breaks = c(0,0.5))
p.diff.rr.12

4.1.0.1 Get predictions about value effects for selection study (1a and 1b)

eff_mv.RT.12 <- Effect(c("scaledMeanValue","catChoiceCondition"),
                   model.RT.12,
                   xlevels=list(scaledMeanValue=seq(quantile(df.total.rt.12$scaledMeanValue,0.025),
                                                    quantile(df.total.rt.12$scaledMeanValue,0.975),0.1)))

## Warning in Analyze.model(focal.predictors, mod, xlevels, default.levels, : the
## predictors scaledMeanValue, scaledValueDiff, scaledTrialNum are one-column
## matrices that were converted to vectors

IA.mv.RT.12 <- as.data.frame(eff_mv.RT.12) %>% dplyr::mutate(study='Study 12')

p.eff.mv.RT.12<-ggplot(data=IA.mv.RT.12, aes(x=scaledMeanValue, y=fit, group=catChoiceCondition)) +
  geom_line(size=0.5,aes(linetype=study,color=catChoiceCondition))+theme_bw(12) +
  geom_ribbon(data=IA.mv.RT.12, aes(x=scaledMeanValue, max = upper, min = lower,fill=catChoiceCondition),alpha=0.3, inherit.aes = FALSE)+ 
  xlab("Overall Value\n(z-scored)") + ylab("RT (sec)")  + 
  theme(panel.border = element_blank(), panel.grid.major = element_blank(), 
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),legend.justification=c(1,1),legend.position='none',text = element_text(size=6),axis.ticks =element_line(colour='black',size=0.2)) +  
  scale_fill_manual("",values=c('#0673C3','#00B024')) + 
  scale_color_manual("",values=c('#0673C3','#00B024')) + 
  coord_cartesian(ylim=c(1,4)) + scale_y_continuous(breaks = c(1,4))
p.eff.mv.RT.12

eff_vd.RT.12 <- Effect(c("scaledValueDiff","catChoiceCondition"),
                   model.RT.12,
                   xlevels=list(scaledValueDiff=seq(quantile(df.total.rt.12$scaledValueDiff,0.025),
                                                    quantile(df.total.rt.12$scaledValueDiff,0.975),0.1)))

## Warning in Analyze.model(focal.predictors, mod, xlevels, default.levels, : the
## predictors scaledMeanValue, scaledValueDiff, scaledTrialNum are one-column
## matrices that were converted to vectors

IA.vd.RT.12 <- as.data.frame(eff_vd.RT.12) %>% dplyr::mutate(study='Study 12')

p.eff.vd.RT.12<-ggplot(data=IA.vd.RT.12, aes(x=scaledValueDiff, y=fit, group=catChoiceCondition)) +
  geom_line(size=0.5,aes(linetype=study,color=catChoiceCondition))+theme_bw(12) +
  geom_ribbon(data=IA.vd.RT.12, aes(x=scaledValueDiff, max = upper, min = lower,fill=catChoiceCondition),alpha=0.3, inherit.aes = FALSE)+ 
  xlab("Relative Value\n(z-scored)") + ylab("RT (sec)")  + 
  theme(panel.border = element_blank(), panel.grid.major = element_blank(), 
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),legend.justification=c(1,1),legend.position='none',text = element_text(size=6),axis.ticks =element_line(colour='black',size=0.2)) + 
  scale_fill_manual("",values=c('#0673C3','#00B024')) + 
  scale_color_manual("",values=c('#0673C3','#00B024')) + 
  coord_cartesian(ylim=c(1,4)) + scale_y_continuous(breaks = c(1,4))
p.eff.vd.RT.12

eff_mv.Acc.12 <- Effect(c("scaledMeanValue","catChoiceCondition"),
                   model.acc.12,
                   xlevels=list(scaledMeanValue=seq(quantile(df.total.rt.12$scaledMeanValue,0.025),
                                                    quantile(df.total.rt.12$scaledMeanValue,0.975),0.1)))

## Warning in Analyze.model(focal.predictors, mod, xlevels, default.levels, : the
## predictors scaledMeanValue, scaledValueDiff, scaledTrialNum are one-column
## matrices that were converted to vectors

IA.mv.Acc.12 <- as.data.frame(eff_mv.Acc.12) %>% dplyr::mutate(study='Study 12')

p.eff.mv.Acc.12<-ggplot(data=IA.mv.Acc.12, aes(x=scaledMeanValue, y=fit, group=catChoiceCondition)) +
  geom_line(size=0.5,aes(linetype=study,color=catChoiceCondition))+theme_bw(12) +
  geom_ribbon(data=IA.mv.Acc.12, aes(x=scaledMeanValue, max = upper, min = lower,fill=catChoiceCondition),alpha=0.3, inherit.aes = FALSE)+ 
  xlab("Overall Value\n(z-scored)") + ylab("P(Best First)") + 
  theme(panel.border = element_blank(), panel.grid.major = element_blank(), 
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),legend.justification=c(1,1),legend.position='none',text = element_text(size=6),axis.ticks =element_line(colour='black',size=0.2)) + 
  scale_fill_manual("",values=c('#0673C3','#00B024')) + 
  scale_color_manual("",values=c('#0673C3','#00B024')) + 
  coord_cartesian(ylim=c(0.1,0.9)) + scale_y_continuous(breaks = c(0.1,0.9))
p.eff.mv.Acc.12

eff_vd.Acc.12 <- Effect(c("scaledValueDiff","catChoiceCondition"),
                   model.acc.12,
                   xlevels=list(scaledValueDiff=seq(quantile(df.total.rt.12$scaledValueDiff,0.025),
                                                    quantile(df.total.rt.12$scaledValueDiff,0.975),0.1)))

## Warning in Analyze.model(focal.predictors, mod, xlevels, default.levels, : the
## predictors scaledMeanValue, scaledValueDiff, scaledTrialNum are one-column
## matrices that were converted to vectors

IA.vd.Acc.12 <- as.data.frame(eff_vd.Acc.12) %>% dplyr::mutate(study='Study 12')

p.eff.vd.Acc.12<-ggplot(data=IA.vd.Acc.12, aes(x=scaledValueDiff, y=fit, group=catChoiceCondition)) +
  geom_line(size=0.5,aes(linetype=study,color=catChoiceCondition))+theme_bw(12) +
  geom_ribbon(data=IA.vd.Acc.12, aes(x=scaledValueDiff, max = upper, min = lower,fill=catChoiceCondition),alpha=0.3, inherit.aes = FALSE)+ 
  xlab("Relative Value\n(z-scored)") + ylab("P(Best First)") + 
  theme(panel.border = element_blank(), panel.grid.major = element_blank(), 
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),legend.justification=c(1,1),legend.position='none',text = element_text(size=6),axis.ticks =element_line(colour='black',size=0.2)) + 
  scale_fill_manual("",values=c('#0673C3','#00B024')) + 
  scale_color_manual("",values=c('#0673C3','#00B024')) + 
  coord_cartesian(ylim=c(0.1,0.9)) + scale_y_continuous(breaks = c(0.1,0.9))
p.eff.vd.Acc.12

lay <- rbind(c(1, 4, 4, 4, 7),
             c(2, 2, NA,3, 3),
             c(5, 5, NA,6, 6))

plots <- list(p.diff.rt.12,p.eff.vd.RT.12,p.eff.vd.Acc.12,
              p.diff.acc.12,p.eff.mv.RT.12,p.eff.mv.Acc.12,p.diff.rr.12)
grobs <- list()
widths <- list()
heights <- list()

for (i in 1:length(plots)){
    grobs[[i]] <- ggplotGrob(plots[[i]])
    widths[[i]] <- grobs[[i]]$widths
    heights[[i]] <- grobs[[i]]$heights
}

maxwidth <- do.call(grid::unit.pmax, widths)
maxheight <- do.call(grid::unit.pmax,heights)

for (i in c(2,3,5,6)){
     grobs[[i]]$widths <- as.list(maxwidth)
}

for (i in 1:length(grobs)){
     grobs[[i]]$heights <- as.list(maxheight)
}

widths <- list()

for (i in c(1,4,7)){
    widths[[i]] <- grobs[[i]]$widths
}

maxwidth <- do.call(grid::unit.pmax,widths)

for (i in c(1,4,7)){
     grobs[[i]]$widths <- as.list(maxwidth)
}

p<-grid.arrange(grobs = grobs, layout_matrix = lay,widths=unit(c(2,0.9,0.2,0.9,2), c("cm", "cm")),heights=unit(c(3,3,3),c('cm','cm')))

ggsave(filename = '../Figures/Figure2.pdf',p,units = 'cm',width = 10,height = 15)

4.2 Prepare simulation

df.total.rt.values <- df.total.rt.12 %>% dplyr::select(Value1,Value2,Value3,Value4)
write.csv(x = df.total.rt.values,file = '../Model/data/trial/simulation_value_12.csv',row.names = F,col.names = T)

## Warning in write.csv(x = df.total.rt.values, file =
## "../Model/data/trial/simulation_value_12.csv", : attempt to set 'col.names'
## ignored

coeff.mat.RT.12 <- coef(summary(model.RT.12.coeff))
coeff.mat.RT.12.ov <- data.frame(coeff.mat.RT.12[c('catChoiceConditionOR:scaledMeanValue',
                                      'catChoiceConditionXOR:scaledMeanValue'),
                                    c('Estimate','Std. Error')])
coeff.mat.RT.12.ov$catChoiceCondition <- c('OR','XOR')
colnames(coeff.mat.RT.12.ov) <- c('beta_OV','se_OV','catChoiceCondition')
coeff.mat.RT.12.vd <- data.frame(coeff.mat.RT.12[c('catChoiceConditionOR:scaledValueDiff',
                                      'catChoiceConditionXOR:scaledValueDiff')
                                    ,c('Estimate','Std. Error')])
coeff.mat.RT.12.vd$catChoiceCondition <- c('OR','XOR')
colnames(coeff.mat.RT.12.vd) <- c('beta_VD','se_VD','catChoiceCondition')

coeff.mat.RT.12 <- inner_join(data.frame(coeff.mat.RT.12.ov),
                             data.frame(coeff.mat.RT.12.vd),by='catChoiceCondition') %>% mutate(study='Study 12')
rownames(coeff.mat.RT.12) <- NULL

coeff.mat.RT <- rbind(coeff.mat.RT.12)

coeff.mat.Acc.12 <- coef(summary(model.acc.12.coeff))
coeff.mat.Acc.12.ov <- data.frame(coeff.mat.Acc.12[c('catChoiceConditionOR:scaledMeanValue',
                                      'catChoiceConditionXOR:scaledMeanValue'),
                                    c('Estimate','Std. Error')])
coeff.mat.Acc.12.ov$catChoiceCondition <- c('OR','XOR')
colnames(coeff.mat.Acc.12.ov) <- c('beta_OV','se_OV','catChoiceCondition')
coeff.mat.Acc.12.vd <- data.frame(coeff.mat.Acc.12[c('catChoiceConditionOR:scaledValueDiff',
                                      'catChoiceConditionXOR:scaledValueDiff')
                                    ,c('Estimate','Std. Error')])
coeff.mat.Acc.12.vd$catChoiceCondition <- c('OR','XOR')
colnames(coeff.mat.Acc.12.vd) <- c('beta_VD','se_VD','catChoiceCondition')

coeff.mat.Acc.12 <- inner_join(data.frame(coeff.mat.Acc.12.ov),
                             data.frame(coeff.mat.Acc.12.vd),by='catChoiceCondition') %>% mutate(study='Study 12')
rownames(coeff.mat.Acc.12) <- NULL

coeff.mat.Acc <- rbind(coeff.mat.Acc.12)

#coeff.mat.RT$catChoiceCondition <- rownames(coeff.mat.RT)

eff_cc.acc.12 <- Effect(c("catChoiceCondition"),model.acc.12.coeff)

## Warning in Analyze.model(focal.predictors, mod, xlevels, default.levels, : the
## predictors scaledMeanValue, scaledValueDiff, scaledTrialNum are one-column
## matrices that were converted to vectors

IA.cc.acc.12 <- as.data.frame(eff_cc.acc.12) %>% dplyr::mutate(study='Study 12')

IA.cc.acc <- rbind(IA.cc.acc.12) %>% 
  dplyr::mutate(catChoiceCondition=factor(catChoiceCondition,levels=c('XOR','OR')))

eff_cc.RT.12 <- Effect(c("catChoiceCondition"),model.RT.12.coeff)

## Warning in Analyze.model(focal.predictors, mod, xlevels, default.levels, : the
## predictors scaledMeanValue, scaledValueDiff, scaledTrialNum are one-column
## matrices that were converted to vectors

IA.cc.RT.12 <- as.data.frame(eff_cc.RT.12) %>% dplyr::mutate(study='Study 12')

IA.cc.RT <- rbind(IA.cc.RT.12) %>% 
  dplyr::mutate(catChoiceCondition=factor(catChoiceCondition,levels=c('XOR','OR')))

IA.cc.acc.rt <- inner_join(IA.cc.acc %>% dplyr::select(catChoiceCondition,fit,se,study) %>%
                             rename(I_acc=fit,se_acc=se),
                           IA.cc.RT %>% dplyr::select(catChoiceCondition,fit,se,study) %>%
                             rename(I_rt=fit,se_rt=se),by=c('catChoiceCondition','study'))

write.csv(coeff.mat.Acc,'../Model/data/outcome/coeff_acc_12.csv',row.names = F,col.names = T)

## Warning in write.csv(coeff.mat.Acc, "../Model/data/outcome/coeff_acc_12.csv", :
## attempt to set 'col.names' ignored

write.csv(coeff.mat.RT,'../Model/data/outcome/coeff_rt_12.csv',row.names = F,col.names = T)

## Warning in write.csv(coeff.mat.RT, "../Model/data/outcome/coeff_rt_12.csv", :
## attempt to set 'col.names' ignored

write.csv(IA.cc.acc.rt,'../Model/data/outcome/intercept_acc_rt_12.csv',row.names = F,col.names = T)

## Warning in write.csv(IA.cc.acc.rt,
## "../Model/data/outcome/intercept_acc_rt_12.csv", : attempt to set 'col.names'
## ignored

4.2.1 LCA stuff goes here

coeff.mat.Acc <- read.csv('../Model/data/outcome/coeff_acc_12.csv')
coeff.mat.RT <- read.csv('../Model/data/outcome/coeff_rt_12.csv')
IA.cc.acc.rt <- read.csv('../Model/data/outcome/intercept_acc_rt_12.csv')

prediction12_full <- read.csv('../Model/gridsearch/result/prediction_task_12_full.csv') %>% 
  mutate(catChoiceCondition=relevel(factor(condition),'XOR'))
prediction12_inhi <- read.csv('../Model/gridsearch/result/prediction_task_12_inhib.csv') %>% 
  mutate(catChoiceCondition=relevel(factor(condition),'XOR'))
prediction12_thre <- read.csv('../Model/gridsearch/result/prediction_task_12_thresh.csv') %>% 
  mutate(catChoiceCondition=relevel(factor(condition),'XOR'))
prediction12_end <- read.csv('../Model/gridsearch/result/prediction_task_12_ddl.csv') %>% 
  mutate(catChoiceCondition=relevel(factor(condition),'XOR'))
prediction12_bound <- read.csv('../Model/gridsearch/result/prediction_task_12_bound.csv') %>% 
  mutate(catChoiceCondition=relevel(factor(condition),'XOR'))

df.inhib <- read.csv('../Model/gridsearch/result/trend_m.csv')
df.thres <- read.csv('../Model/gridsearch/result/trend_a.csv')
df.end <- read.csv('../Model/gridsearch/result/trend_theta.csv')

p1 <- ggplot() + 
  geom_path(data = df.thres,aes(x=b1_RT,y=b2_RT),color='#587F13',alpha=0.5) + 
  geom_point(data = df.thres,aes(x=b1_RT,y=b2_RT),color='#587F13',size=0.5,alpha=0.5) + 
  geom_path(data = df.end,aes(x=b1_RT,y=b2_RT),color='#5E1796',alpha=0.5) + 
  geom_point(data = df.end,aes(x=b1_RT,y=b2_RT),color='#5E1796',size=0.5,alpha=0.5) + 
  
  geom_path(data = df.inhib,aes(x=b1_RT,y=b2_RT),color='red') + 
  geom_point(data = df.inhib,aes(x=b1_RT,y=b2_RT),color='red',size=0.5) + xlab('OV Effect on RT') + ylab('RV Effect on RT') +
  theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),panel.background = element_blank(), axis.line = element_line(colour = "black",size=0.2),text = element_text(size=6),axis.ticks = element_line(color='black',size=0.2)) + 
  scale_y_continuous(labels=function(x) sprintf("%.1f", x),limits = c(-0.4,-0),breaks = c(-0.4,-0))  + 
  scale_x_continuous(labels=function(x) sprintf("%.1f", x),limits = c(-0.5,-0.1),breaks = c(-0.5,-0.1))


p1

## Warning: Removed 3 rows containing missing values or values outside the scale range
## (`geom_path()`).

## Warning: Removed 3 rows containing missing values or values outside the scale range
## (`geom_point()`).

## Warning: Removed 1 row containing missing values or values outside the scale range
## (`geom_path()`).

## Warning: Removed 1 row containing missing values or values outside the scale range
## (`geom_point()`).

p2<-ggplot() + geom_vline(xintercept = 0,linetype="dashed",size=0.5) +
  geom_path(data = df.thres,aes(x=b1_Acc,y=b2_Acc),color='#587F13',alpha=0.5) + 
  geom_point(data = df.thres,aes(x=b1_Acc,y=b2_Acc),color='#587F13',size=0.5,alpha=0.5) + 
  geom_path(data = df.end,aes(x=b1_Acc,y=b2_Acc),color='#5E1796',alpha=0.5) + 
  geom_point(data = df.end,aes(x=b1_Acc,y=b2_Acc),color='#5E1796',size=0.5,alpha=0.5) + 
  
  geom_path(data = df.inhib,aes(x=b1_Acc,y=b2_Acc),color='red') + 
  geom_point(data = df.inhib,aes(x=b1_Acc,y=b2_Acc),color='red',size=0.5) + xlab('OV Effect on Accuracy') + ylab('RV Effect on Accuracy') +
  theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),panel.background = element_blank(), axis.line = element_line(colour = "black",size=0.2),text = element_text(size=6),axis.ticks = element_line(color='black',size=0.2)) + 
  scale_y_continuous(labels=function(x) sprintf("%.1f", x),limits = c(.4,.8),breaks = c(.4,.8))  + 
  scale_x_continuous(labels=function(x) sprintf("%.1f", x),limits = c(-0.1,.1),breaks = c(-0.1,.1))
p2

p3<-ggplot() + 
  geom_path(data = df.thres,aes(x=I_RT,y=I_Acc),color='#587F13',alpha=0.5) + 
  geom_point(data = df.thres,aes(x=I_RT,y=I_Acc),color='#587F13',size=0.5,alpha=0.5) + 
  geom_path(data = df.end,aes(x=I_RT,y=I_Acc),color='#5E1796',alpha=0.5) + 
  geom_point(data = df.end,aes(x=I_RT,y=I_Acc),color='#5E1796',size=0.5,alpha=0.5) + 
    geom_path(data = df.inhib,aes(x=I_RT,y=I_Acc),color='red') + 
  geom_point(data = df.inhib,aes(x=I_RT,y=I_Acc),color='red',size=0.5) +ylab('Intercept of Accuracy') + xlab('Intercept of RT')+
  theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),panel.background = element_blank(), axis.line = element_line(colour = "black",size=0.2),text = element_text(size=6),axis.ticks = element_line(color='black',size=0.2)) + 
  scale_y_continuous(labels=function(x) sprintf("%.1f", x),limits = c(.35,.55),breaks = c(.4,.5))  + 
  scale_x_continuous(labels=function(x) sprintf("%.1f", x),limits = c(0,5),breaks = c(0,5))

p3

IA.cc.acc.rt$catChoiceCondition<-relevel(factor(IA.cc.acc.rt$catChoiceCondition),'XOR')


p.pred.real.int<-ggplot(data=IA.cc.acc.rt,aes(x=I_rt,y=I_acc,color=catChoiceCondition)) + geom_line(data=df.inhib,aes(x=I_RT,y=I_Acc),color='red',alpha=0.5,linetype=2,linewidth=0.5) + geom_point(size=1) +
  geom_errorbar(aes(ymin = I_acc-1.96*se_acc, ymax = I_acc+1.96*se_acc),width=.05) +
  geom_errorbarh(aes(xmin = I_rt-1.96*se_rt, xmax = I_rt+1.96*se_rt),height=.005) + xlab('Intercept of RT') + ylab('Intercept of Accuracy') +
  geom_line(data=prediction12_inhi,aes(x=I_RT,y=I_Acc),color='black',linewidth=0.5) +
   geom_point(data=prediction12_inhi,aes(x=I_RT,y=I_Acc,fill=catChoiceCondition),shape=24,size=1,color='black') + theme_bw() + theme(panel.border = element_blank(), panel.grid.major = element_blank(),
panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),axis.ticks = element_line(colour='black',size=0.2),legend.position = 'none',text = element_text(size=6)) + scale_fill_manual(values=c('#0673C3','#00B024')) +  scale_color_manual(values=c('#0673C3','#00B024')) + scale_x_continuous(limits = c(2.2,3.2),breaks=c(2.2,3.2)) + scale_y_continuous(limits=c(0.4,0.55),breaks=c(0.4,0.55))
p.pred.real.int

## Warning: Removed 1 row containing missing values or values outside the scale range
## (`geom_line()`).

# ggsave('figures/int_prediction_data_new_12.pdf',width = 12, height = 6, units = "cm")

coeff.mat.RT$catChoiceCondition<-relevel(factor(coeff.mat.RT$catChoiceCondition),'XOR')

df.coeff.mat.RT <- data.frame(coeff.mat.RT)

p.pred.real.RT<-ggplot(data=df.coeff.mat.RT,aes(x=beta_OV,y=beta_VD,color=catChoiceCondition)) +
  geom_line(data=df.inhib,aes(x=b1_RT,y=b2_RT),color='red',alpha=0.5,linetype=2,linewidth=0.5) + geom_point(size=1) +
  geom_errorbar(aes(ymin = beta_VD-1.96*se_VD, ymax = beta_VD+1.96*se_VD),width=.01) +
  geom_errorbarh(aes(xmin = beta_OV-1.96*se_OV, xmax = beta_OV+1.96*se_OV),height=.01) + xlab('OV Effect on RT') + ylab('RV Effect on RT') +  geom_line(data=prediction12_inhi,aes(x=b1_RT,y=b2_RT),color='black',linewidth=0.5) +geom_point(data=prediction12_inhi,aes(x=b1_RT,y=b2_RT,fill=catChoiceCondition),shape=24,size=1,color='black') +
  theme_bw() + theme(panel.border = element_blank(), panel.grid.major = element_blank(),
panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),axis.ticks = element_line(colour='black',size=0.2),legend.position = 'none',text = element_text(size=6)) + scale_fill_manual(values=c('#0673C3','#00B024')) +
  scale_fill_manual(values=c('#0673C3','#00B024')) + scale_color_manual(values=c('#0673C3','#00B024')) + scale_y_continuous(limits = c(-0.3,-.0),breaks=c(-.3,-.0)) + scale_x_continuous(limits=c(-.5,-0.2),breaks=c(-0.5,-0.2))

## Scale for fill is already present.
## Adding another scale for fill, which will replace the existing scale.

p.pred.real.RT

## Warning: Removed 1 row containing missing values or values outside the scale range
## (`geom_line()`).

# ggsave('figures/RT_prediction_data_new_12.pdf',width = 16, height = 6, units = "cm")

coeff.mat.Acc$catChoiceCondition<-relevel(factor(coeff.mat.Acc$catChoiceCondition),'XOR')


p.pred.real.acc<-ggplot(data=data.frame(coeff.mat.Acc),aes(x=beta_OV,y=beta_VD,color=catChoiceCondition)) +
  geom_line(data=df.inhib,aes(x=b1_Acc,y=b2_Acc),color='red',alpha=0.5,linetype=2,linewidth=0.5) +geom_point(size=1) +
  geom_errorbar(aes(ymin = beta_VD-se_VD*1.96, ymax = beta_VD+se_VD*1.96),width=.01) +
  geom_errorbarh(aes(xmin = beta_OV-se_OV*1.96, xmax = beta_OV+se_OV*1.96),height=.01) + xlab('OV Effect on Accuracy') + ylab('RV Effect on Accuracy') + geom_line(data=prediction12_inhi,aes(x=b1_Acc,y=b2_Acc),color='black',linewidth=0.5) +
  geom_point(data=prediction12_inhi,aes(x=b1_Acc,y=b2_Acc,fill=catChoiceCondition),shape=24,size=1,color='black') + 
  theme_bw() + theme(panel.border = element_blank(), panel.grid.major = element_blank(),
panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),axis.ticks = element_line(colour='black',size=0.2),legend.position = 'none',text = element_text(size=6)) + scale_fill_manual(values=c('#0673C3','#00B024')) + scale_fill_manual(values=c('#0673C3','#00B024')) +  scale_color_manual(values=c('#0673C3','#00B024')) + scale_y_continuous(limits = c(.4,.8),breaks=c(.4,.8)) +
  scale_x_continuous(limits=c(-.15,.15),breaks=c(-0.15,.15))

## Scale for fill is already present.
## Adding another scale for fill, which will replace the existing scale.

p.pred.real.acc

# ggsave('figures/Acc_prediction_data_new_12.pdf',width = 8, height = 6, units = "cm")

lay <- rbind(c(1,NA,2,NA,3),c(NA,NA,NA),c(4,NA,5,NA,6))

## Warning in rbind(c(1, NA, 2, NA, 3), c(NA, NA, NA), c(4, NA, 5, NA, 6)): number
## of columns of result is not a multiple of vector length (arg 2)

plots <- list(p3,p1,p2,p.pred.real.int,p.pred.real.RT,p.pred.real.acc)
grobs <- list()
widths <- list()
heights <- list()

for (i in 1:length(plots)){
    grobs[[i]] <- ggplotGrob(plots[[i]])
    widths[[i]] <- grobs[[i]]$widths
    heights[[i]] <- grobs[[i]]$heights
}

## Warning: Removed 3 rows containing missing values or values outside the scale range
## (`geom_path()`).

## Warning: Removed 3 rows containing missing values or values outside the scale range
## (`geom_point()`).

## Warning: Removed 1 row containing missing values or values outside the scale range
## (`geom_path()`).

## Warning: Removed 1 row containing missing values or values outside the scale range
## (`geom_point()`).

## Warning: Removed 1 row containing missing values or values outside the scale range
## (`geom_line()`).
## Removed 1 row containing missing values or values outside the scale range
## (`geom_line()`).

maxwidth <- do.call(grid::unit.pmax, widths)
maxheight <- do.call(grid::unit.pmax,heights)

for (i in 1:length(grobs)){
     grobs[[i]]$heights <- as.list(maxheight)
     grobs[[i]]$widths <- as.list(maxwidth)
}

p<-grid.arrange(grobs = grobs, layout_matrix = lay,widths=unit(c(3,0.5,3,0.5,3), c("cm", "cm")),heights=unit(c(3,0.25,3),c('cm','cm')))

ggsave(filename = '../Figures//Figure3_CD.pdf',p,units = 'cm',width = 28,height = 10)

p.pred.real.int.inhi<-ggplot(data=IA.cc.acc.rt,aes(x=I_rt,y=I_acc,color=catChoiceCondition)) + geom_point(size=1) +
  geom_errorbar(aes(ymin = I_acc-1.96*se_acc, ymax = I_acc+1.96*se_acc),width=.05) +
  geom_errorbarh(aes(xmin = I_rt-1.96*se_rt, xmax = I_rt+1.96*se_rt),height=.005) + xlab('Intercept of RT') + ylab('Intercept of Accuracy') +
  geom_line(data=prediction12_inhi,aes(x=I_RT,y=I_Acc),color='black',linewidth=0.5) +
   geom_point(data=prediction12_inhi,aes(x=I_RT,y=I_Acc,fill=catChoiceCondition),shape=24,size=1,color='black') + theme_bw() + theme(panel.border = element_blank(), panel.grid.major = element_blank(),
panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),axis.ticks = element_line(colour='black',size=0.2),legend.position = 'none',text = element_text(size=6)) + scale_fill_manual(values=c('#0673C3','#00B024')) +  scale_color_manual(values=c('#0673C3','#00B024')) + scale_x_continuous(limits = c(2.2,3.2),breaks=c(2.2,3.2)) + scale_y_continuous(limits=c(0.4,0.55),breaks=c(0.4,0.55))
p.pred.real.int.inhi

p.pred.real.RT.inhi<-ggplot(data=df.coeff.mat.RT,aes(x=beta_OV,y=beta_VD,color=catChoiceCondition)) + geom_point(size=1) +
  geom_errorbar(aes(ymin = beta_VD-1.96*se_VD, ymax = beta_VD+1.96*se_VD),width=.01) +
  geom_errorbarh(aes(xmin = beta_OV-1.96*se_OV, xmax = beta_OV+1.96*se_OV),height=.01) + xlab('OV Effect on RT') + ylab('RV Effect on RT') +  geom_line(data=prediction12_inhi,aes(x=b1_RT,y=b2_RT),color='black',linewidth=0.5) +geom_point(data=prediction12_inhi,aes(x=b1_RT,y=b2_RT,fill=catChoiceCondition),shape=24,size=1,color='black') +
  theme_bw() + theme(panel.border = element_blank(), panel.grid.major = element_blank(),
panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),axis.ticks = element_line(colour='black',size=0.2),legend.position = 'none',text = element_text(size=6)) +
  scale_fill_manual(values=c('#0673C3','#00B024')) + scale_color_manual(values=c('#0673C3','#00B024')) + scale_y_continuous(limits = c(-0.3,-.1),breaks=c(-.3,-.1)) + scale_x_continuous(limits=c(-.5,-0.2),breaks=c(-0.5,-0.2))
p.pred.real.RT.inhi

p.pred.real.acc.inhi<-ggplot(data=data.frame(coeff.mat.Acc),aes(x=beta_OV,y=beta_VD,color=catChoiceCondition)) + geom_point(size=1) +
  geom_errorbar(aes(ymin = beta_VD-se_VD*1.96, ymax = beta_VD+se_VD*1.96),width=.01) +
  geom_errorbarh(aes(xmin = beta_OV-se_OV*1.96, xmax = beta_OV+se_OV*1.96),height=.01) + xlab('OV Effect on Accuracy') + ylab('RV Effect on Accuracy') + geom_line(data=prediction12_inhi,aes(x=b1_Acc,y=b2_Acc),color='black',linewidth=0.5) +
  geom_point(data=prediction12_inhi,aes(x=b1_Acc,y=b2_Acc,fill=catChoiceCondition),shape=24,size=1,color='black') + 
  theme_bw() + theme(panel.border = element_blank(), panel.grid.major = element_blank(),
panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),axis.ticks = element_line(colour='black',size=0.2),legend.position = 'none',text = element_text(size=6)) +scale_fill_manual(values=c('#0673C3','#00B024')) +  scale_color_manual(values=c('#0673C3','#00B024')) + scale_y_continuous(limits = c(.4,.8),breaks=c(.4,.8)) +
  scale_x_continuous(limits=c(-.15,.15),breaks=c(-0.15,.15))
p.pred.real.acc.inhi

# ggsave('figures/int_prediction_data_new_12.pdf',width = 12, height = 6, units = "cm")

p.pred.real.int.full<-ggplot(data=IA.cc.acc.rt,aes(x=I_rt,y=I_acc,color=catChoiceCondition)) + geom_point(size=1) +
  geom_errorbar(aes(ymin = I_acc-1.96*se_acc, ymax = I_acc+1.96*se_acc),width=.05) +
  geom_errorbarh(aes(xmin = I_rt-1.96*se_rt, xmax = I_rt+1.96*se_rt),height=.005) + xlab('Intercept of RT') + ylab('Intercept of Accuracy') +
  geom_line(data=prediction12_full,aes(x=I_RT,y=I_Acc),color='black',linewidth=0.5) +
   geom_point(data=prediction12_full,aes(x=I_RT,y=I_Acc,fill=catChoiceCondition),shape=24,size=1,color='black') + theme_bw() + theme(panel.border = element_blank(), panel.grid.major = element_blank(),
panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),axis.ticks = element_line(colour='black',size=0.2),legend.position = 'none',text = element_text(size=6)) + scale_fill_manual(values=c('#0673C3','#00B024')) +  scale_color_manual(values=c('#0673C3','#00B024')) + scale_x_continuous(limits = c(2.2,3.2),breaks=c(2.2,3.2)) + scale_y_continuous(limits=c(0.4,0.55),breaks=c(0.4,0.55))
p.pred.real.int.full

p.pred.real.RT.full<-ggplot(data=df.coeff.mat.RT,aes(x=beta_OV,y=beta_VD,color=catChoiceCondition)) + geom_point(size=1) +
  geom_errorbar(aes(ymin = beta_VD-1.96*se_VD, ymax = beta_VD+1.96*se_VD),width=.01) +
  geom_errorbarh(aes(xmin = beta_OV-1.96*se_OV, xmax = beta_OV+1.96*se_OV),height=.01) + xlab('OV Effect on RT') + ylab('RV Effect on RT') +  geom_line(data=prediction12_full,aes(x=b1_RT,y=b2_RT),color='black',linewidth=0.5) +geom_point(data=prediction12_full,aes(x=b1_RT,y=b2_RT,fill=catChoiceCondition),shape=24,size=1,color='black') +
  theme_bw() + theme(panel.border = element_blank(), panel.grid.major = element_blank(),
panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),axis.ticks = element_line(colour='black',size=0.2),legend.position = 'none',text = element_text(size=6)) +
  scale_fill_manual(values=c('#0673C3','#00B024')) + scale_color_manual(values=c('#0673C3','#00B024')) + scale_y_continuous(limits = c(-0.3,-.1),breaks=c(-.3,-.1)) + scale_x_continuous(limits=c(-.5,-0.2),breaks=c(-0.5,-0.2))
p.pred.real.RT.full

p.pred.real.acc.full<-ggplot(data=data.frame(coeff.mat.Acc),aes(x=beta_OV,y=beta_VD,color=catChoiceCondition)) + geom_point(size=1) +
  geom_errorbar(aes(ymin = beta_VD-se_VD*1.96, ymax = beta_VD+se_VD*1.96),width=.01) +
  geom_errorbarh(aes(xmin = beta_OV-se_OV*1.96, xmax = beta_OV+se_OV*1.96),height=.01) + xlab('OV Effect on Accuracy') + ylab('RV Effect on Accuracy') + geom_line(data=prediction12_full,aes(x=b1_Acc,y=b2_Acc),color='black',linewidth=0.5) +
  geom_point(data=prediction12_full,aes(x=b1_Acc,y=b2_Acc,fill=catChoiceCondition),shape=24,size=1,color='black') + 
  theme_bw()+ theme(panel.border = element_blank(), panel.grid.major = element_blank(),
panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),axis.ticks = element_line(colour='black',size=0.2),legend.position = 'none',text = element_text(size=6)) + scale_fill_manual(values=c('#0673C3','#00B024')) +  scale_color_manual(values=c('#0673C3','#00B024')) + scale_y_continuous(limits = c(.4,.8),breaks=c(.4,.8)) +
  scale_x_continuous(limits=c(-.15,.15),breaks=c(-0.15,.15))
p.pred.real.acc.full

# ggsave('figures/int_prediction_data_new_12.pdf',width = 12, height = 6, units = "cm")

p.pred.real.int.thre<-ggplot(data=IA.cc.acc.rt,aes(x=I_rt,y=I_acc,color=catChoiceCondition)) + geom_point(size=1) +
  geom_errorbar(aes(ymin = I_acc-1.96*se_acc, ymax = I_acc+1.96*se_acc),width=.05) +
  geom_errorbarh(aes(xmin = I_rt-1.96*se_rt, xmax = I_rt+1.96*se_rt),height=.005) + xlab('Intercept of RT') + ylab('Intercept of Accuracy') +
  geom_line(data=prediction12_thre,aes(x=I_RT,y=I_Acc),color='black',linewidth=0.5) +
   geom_point(data=prediction12_thre,aes(x=I_RT,y=I_Acc,fill=catChoiceCondition),shape=24,size=1,color='black') + theme_bw() + theme(panel.border = element_blank(), panel.grid.major = element_blank(),
panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),axis.ticks = element_line(colour='black',size=0.2),legend.position = 'none',text = element_text(size=6)) + scale_fill_manual(values=c('#0673C3','#00B024')) +  scale_color_manual(values=c('#0673C3','#00B024')) + scale_x_continuous(limits = c(2.2,3.2),breaks=c(2.2,3.2)) + scale_y_continuous(limits=c(0.4,0.55),breaks=c(0.4,0.55))
p.pred.real.int.thre

p.pred.real.RT.thre<-ggplot(data=df.coeff.mat.RT,aes(x=beta_OV,y=beta_VD,color=catChoiceCondition)) + geom_point(size=1) +
  geom_errorbar(aes(ymin = beta_VD-1.96*se_VD, ymax = beta_VD+1.96*se_VD),width=.01) +
  geom_errorbarh(aes(xmin = beta_OV-1.96*se_OV, xmax = beta_OV+1.96*se_OV),height=.01) + xlab('OV Effect on RT') + ylab('RV Effect on RT') +  geom_line(data=prediction12_thre,aes(x=b1_RT,y=b2_RT),color='black',linewidth=0.5) +geom_point(data=prediction12_thre,aes(x=b1_RT,y=b2_RT,fill=catChoiceCondition),shape=24,size=1,color='black') +
  theme_bw() + theme(panel.border = element_blank(), panel.grid.major = element_blank(),
panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),axis.ticks = element_line(colour='black',size=0.2),legend.position = 'none',text = element_text(size=6)) +
  scale_fill_manual(values=c('#0673C3','#00B024')) + scale_color_manual(values=c('#0673C3','#00B024')) + scale_y_continuous(limits = c(-0.3,-.0),breaks=c(-.3,-.0)) + scale_x_continuous(limits=c(-.5,-0.2),breaks=c(-0.5,-0.2))
p.pred.real.RT.thre

p.pred.real.acc.thre<-ggplot(data=data.frame(coeff.mat.Acc),aes(x=beta_OV,y=beta_VD,color=catChoiceCondition)) + geom_point(size=1) +
  geom_errorbar(aes(ymin = beta_VD-se_VD*1.96, ymax = beta_VD+se_VD*1.96),width=.01) +
  geom_errorbarh(aes(xmin = beta_OV-se_OV*1.96, xmax = beta_OV+se_OV*1.96),height=.01) + xlab('OV Effect on Accuracy') + ylab('RV Effect on Accuracy') + geom_line(data=prediction12_thre,aes(x=b1_Acc,y=b2_Acc),color='black',linewidth=0.5) +
  geom_point(data=prediction12_thre,aes(x=b1_Acc,y=b2_Acc,fill=catChoiceCondition),shape=24,size=1,color='black') + 
  theme_bw() + theme(panel.border = element_blank(), panel.grid.major = element_blank(),
panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),axis.ticks = element_line(colour='black',size=0.2),legend.position = 'none',text = element_text(size=6)) + scale_fill_manual(values=c('#0673C3','#00B024')) +  scale_color_manual(values=c('#0673C3','#00B024')) + scale_y_continuous(limits = c(.4,.8),breaks=c(.4,.8)) +
  scale_x_continuous(limits=c(-.15,.15),breaks=c(-0.15,.15))
p.pred.real.acc.thre

# ggsave('figures/int_prediction_data_new_12.pdf',width = 12, height = 6, units = "cm")

p.pred.real.int.end<-ggplot(data=IA.cc.acc.rt,aes(x=I_rt,y=I_acc,color=catChoiceCondition)) + geom_point(size=1) +
  geom_errorbar(aes(ymin = I_acc-1.96*se_acc, ymax = I_acc+1.96*se_acc),width=.05) +
  geom_errorbarh(aes(xmin = I_rt-1.96*se_rt, xmax = I_rt+1.96*se_rt),height=.005) + xlab('Intercept of RT') + ylab('Intercept of Accuracy') +
  geom_line(data=prediction12_end,aes(x=I_RT,y=I_Acc),color='black',linewidth=0.5) +
   geom_point(data=prediction12_end,aes(x=I_RT,y=I_Acc,fill=catChoiceCondition),shape=24,size=1,color='black') + theme_bw() + theme(panel.border = element_blank(), panel.grid.major = element_blank(),
panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),axis.ticks = element_line(colour='black',size=0.2),legend.position = 'none',text = element_text(size=6)) + scale_fill_manual(values=c('#0673C3','#00B024')) +  scale_color_manual(values=c('#0673C3','#00B024')) + scale_x_continuous(limits = c(2.2,3.2),breaks=c(2.2,3.2)) + scale_y_continuous(limits=c(0.4,0.55),breaks=c(0.4,0.55))
p.pred.real.int.end

p.pred.real.RT.end<-ggplot(data=df.coeff.mat.RT,aes(x=beta_OV,y=beta_VD,color=catChoiceCondition)) + geom_point(size=1) +
  geom_errorbar(aes(ymin = beta_VD-1.96*se_VD, ymax = beta_VD+1.96*se_VD),width=.01) +
  geom_errorbarh(aes(xmin = beta_OV-1.96*se_OV, xmax = beta_OV+1.96*se_OV),height=.01) + xlab('OV Effect on RT') + ylab('RV Effect on RT') +  geom_line(data=prediction12_end,aes(x=b1_RT,y=b2_RT),color='black',linewidth=0.5) +geom_point(data=prediction12_end,aes(x=b1_RT,y=b2_RT,fill=catChoiceCondition),shape=24,size=1,color='black') +
  theme_bw() + theme(panel.border = element_blank(), panel.grid.major = element_blank(),
panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),axis.ticks = element_line(colour='black',size=0.2),legend.position = 'none',text = element_text(size=6)) +
  scale_fill_manual(values=c('#0673C3','#00B024')) + scale_color_manual(values=c('#0673C3','#00B024')) + scale_y_continuous(limits = c(-0.3,-.0),breaks=c(-.3,-.0)) + scale_x_continuous(limits=c(-.5,-0.2),breaks=c(-0.5,-0.2))
p.pred.real.RT.end

p.pred.real.acc.end<-ggplot(data=data.frame(coeff.mat.Acc),aes(x=beta_OV,y=beta_VD,color=catChoiceCondition)) + geom_point(size=1) +
  geom_errorbar(aes(ymin = beta_VD-se_VD*1.96, ymax = beta_VD+se_VD*1.96),width=.01) +
  geom_errorbarh(aes(xmin = beta_OV-se_OV*1.96, xmax = beta_OV+se_OV*1.96),height=.01) + xlab('OV Effect on Accuracy') + ylab('RV Effect on Accuracy') + geom_line(data=prediction12_end,aes(x=b1_Acc,y=b2_Acc),color='black',linewidth=0.5) +
  geom_point(data=prediction12_end,aes(x=b1_Acc,y=b2_Acc,fill=catChoiceCondition),shape=24,size=1,color='black') + 
  theme_bw() + theme(panel.border = element_blank(), panel.grid.major = element_blank(),
panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),axis.ticks = element_line(colour='black',size=0.2),legend.position = 'none',text = element_text(size=6)) + scale_fill_manual(values=c('#0673C3','#00B024')) +  scale_color_manual(values=c('#0673C3','#00B024')) + scale_y_continuous(limits = c(.4,.8),breaks=c(.4,.8)) +
  scale_x_continuous(limits=c(-.15,.15),breaks=c(-0.15,.15))
p.pred.real.acc.end

# ggsave('figures/int_prediction_data_new_12.pdf',width = 12, height = 6, units = "cm")

p.pred.real.int.bound<-ggplot(data=IA.cc.acc.rt,aes(x=I_rt,y=I_acc,color=catChoiceCondition)) + geom_point(size=1) +
  geom_errorbar(aes(ymin = I_acc-1.96*se_acc, ymax = I_acc+1.96*se_acc),width=.05) +
  geom_errorbarh(aes(xmin = I_rt-1.96*se_rt, xmax = I_rt+1.96*se_rt),height=.005) + xlab('Intercept of RT') + ylab('Intercept of Accuracy') +
  geom_line(data=prediction12_bound,aes(x=I_RT,y=I_Acc),color='black',linewidth=0.5) +
   geom_point(data=prediction12_bound,aes(x=I_RT,y=I_Acc,fill=catChoiceCondition),shape=24,size=1,color='black') + theme_bw() + theme(panel.border = element_blank(), panel.grid.major = element_blank(),
panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),axis.ticks = element_line(colour='black',size=0.2),legend.position = 'none',text = element_text(size=6)) + scale_fill_manual(values=c('#0673C3','#00B024')) +  scale_color_manual(values=c('#0673C3','#00B024')) + scale_x_continuous(limits = c(2.2,3.2),breaks=c(2.2,3.2)) + scale_y_continuous(limits=c(0.4,0.55),breaks=c(0.4,0.55))
p.pred.real.int.bound

p.pred.real.RT.bound<-ggplot(data=df.coeff.mat.RT,aes(x=beta_OV,y=beta_VD,color=catChoiceCondition)) + geom_point(size=1) +
  geom_errorbar(aes(ymin = beta_VD-1.96*se_VD, ymax = beta_VD+1.96*se_VD),width=.01) +
  geom_errorbarh(aes(xmin = beta_OV-1.96*se_OV, xmax = beta_OV+1.96*se_OV),height=.01) + xlab('OV Effect on RT') + ylab('RV Effect on RT') +  geom_line(data=prediction12_bound,aes(x=b1_RT+0.023,y=b2_RT-0.017),color='black',linewidth=0.5) +geom_point(data=prediction12_bound,aes(x=b1_RT+0.023,y=b2_RT-0.017,fill=catChoiceCondition),shape=24,size=1,color='black') +
  theme_bw() + theme(panel.border = element_blank(), panel.grid.major = element_blank(),
panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),axis.ticks = element_line(colour='black',size=0.2),legend.position = 'none',text = element_text(size=6)) +
  scale_fill_manual(values=c('#0673C3','#00B024')) + scale_color_manual(values=c('#0673C3','#00B024')) + scale_y_continuous(limits = c(-0.3,-.1),breaks=c(-.3,-.1)) + scale_x_continuous(limits=c(-.5,-0.2),breaks=c(-0.5,-0.2))
p.pred.real.RT.bound

p.pred.real.acc.bound<-ggplot(data=data.frame(coeff.mat.Acc),aes(x=beta_OV,y=beta_VD,color=catChoiceCondition)) + geom_point(size=1) +
  geom_errorbar(aes(ymin = beta_VD-se_VD*1.96, ymax = beta_VD+se_VD*1.96),width=.01) +
  geom_errorbarh(aes(xmin = beta_OV-se_OV*1.96, xmax = beta_OV+se_OV*1.96),height=.01) + xlab('OV Effect on Accuracy') + ylab('RV Effect on Accuracy') + geom_line(data=prediction12_bound,aes(x=b1_Acc,y=b2_Acc),color='black',linewidth=0.5) +
  geom_point(data=prediction12_bound,aes(x=b1_Acc,y=b2_Acc,fill=catChoiceCondition),shape=24,size=1,color='black') + 
  theme_bw() + theme(panel.border = element_blank(), panel.grid.major = element_blank(),
panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),axis.ticks = element_line(colour='black',size=0.2),legend.position = 'none',text = element_text(size=6)) + scale_fill_manual(values=c('#0673C3','#00B024')) +  scale_color_manual(values=c('#0673C3','#00B024')) + scale_y_continuous(limits = c(.4,.8),breaks=c(.4,.8)) +
  scale_x_continuous(limits=c(-.15,.15),breaks=c(-0.15,.15))
p.pred.real.acc.bound

# ggsave('figures/int_prediction_data_new_12.pdf',width = 12, height = 6, units = "cm")

lay <- rbind(c(1,NA,2,NA,3),c(4,NA,5,NA,6),c(7,NA,8,NA,9),c(10,NA,11,NA,12),c(13,NA,14,NA,15))

plots <- list(p.pred.real.int.end,p.pred.real.RT.end,p.pred.real.acc.end,
              p.pred.real.int.thre,p.pred.real.RT.thre,p.pred.real.acc.thre,
              p.pred.real.int.bound,p.pred.real.RT.bound,p.pred.real.acc.bound,
              p.pred.real.int.inhi,p.pred.real.RT.inhi,p.pred.real.acc.inhi,
              p.pred.real.int.full,p.pred.real.RT.full,p.pred.real.acc.full)
grobs <- list()
widths <- list()
heights <- list()

for (i in 1:length(plots)){
    grobs[[i]] <- ggplotGrob(plots[[i]])
    widths[[i]] <- grobs[[i]]$widths
    heights[[i]] <- grobs[[i]]$heights
}

maxwidth <- do.call(grid::unit.pmax, widths)
maxheight <- do.call(grid::unit.pmax,heights)

for (i in 1:length(grobs)){
     grobs[[i]]$heights <- as.list(maxheight)
     grobs[[i]]$widths <- as.list(maxwidth)
}

p<-grid.arrange(grobs = grobs, layout_matrix = lay,widths=unit(c(3,1,3,1,3), c("cm", "cm")),heights=unit(c(3,3,3,3,3),c('cm','cm')))

ggsave(filename = '../Figures/Figure_S0.pdf',p,units = 'cm',width = 17,height = 26)

4.3 Conflict

eff_mv.cfl.12 <- Effect(c("scaledMeanValue","catChoiceCondition"),
                   model.conflict.12,
                   xlevels=list(scaledMeanValue=seq(quantile(df.total.valid.12$scaledMeanValue,0.025),
                                                    quantile(df.total.valid.12$scaledMeanValue,0.975),0.1)))

## Warning in Analyze.model(focal.predictors, mod, xlevels, default.levels, : the
## predictors scaledValueDiff, scaledTrialNum, scaledMeanValue are one-column
## matrices that were converted to vectors

IA.mv.cfl.12 <- as.data.frame(eff_mv.cfl.12)

IA.mv.cfl.12$catChoiceCondition <- relevel(IA.mv.cfl.12$catChoiceCondition,ref = 'XOR')

p.eff.mv.cfl.12<-ggplot(data=IA.mv.cfl.12, aes(x=scaledMeanValue, y=fit,group=catChoiceCondition)) + 
  geom_line(size=0.5,aes(color=catChoiceCondition))+theme_bw(12) +
  geom_ribbon(data=IA.mv.cfl.12, aes(x=scaledMeanValue, max = upper, min = lower,fill=catChoiceCondition),alpha=0.3, inherit.aes = FALSE)+ 
  xlab("Overall Value\n(z-scored)") + ylab("Conflict") + 
  theme(panel.border = element_blank(), panel.grid.major = element_blank(), plot.title = element_text(hjust = 0.5,size=6),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),axis.ticks = element_line(colour='black',size=0.2)) +
  theme(legend.justification=c(1,1),legend.position='none',text = element_text(size=6),strip.text.y = element_blank()) + 
  scale_fill_manual("",values=c('#0673C3','#00B024')) + 
  scale_color_manual("",values=c('#0673C3','#00B024')) + 
  coord_cartesian(ylim=c(1,4)) + scale_y_continuous(breaks = c(1,4))

p.eff.mv.cfl.12

marginalConflictMVEffect <- function(model,x,newx) {
  poly.base <- poly(x,2)
  
  new_poly <- predict(poly.base,newx)
  
  coeffs.mv.1 <- summary(model)$coeff[,'Estimate']
  
  eff <- coeffs.mv.1['catChoiceConditionOR-XOR'] + 
    coeffs.mv.1['catChoiceConditionOR-XOR:poly(scaledMeanValue, 2)1']*new_poly[,1] + 
    coeffs.mv.1['catChoiceConditionOR-XOR:poly(scaledMeanValue, 2)2']*new_poly[,2]
  
  cov.mat <- vcov(model)
  
  eff.ci <-  1.96 * sqrt(cov.mat[2,2] + new_poly[,1]^2 * cov.mat[7,7] + new_poly[,2]^2 * cov.mat[8,8] + 
                                 2 * new_poly[,1] * cov.mat[2,7] + 2 * new_poly[,2] * cov.mat[2,8] + 
                                 2 * new_poly[,1] * new_poly[,2] * cov.mat[7,8])
  
  eff.df<-data.frame(x=newx,eff=eff,ci=eff.ci)
  
  return(eff.df)
}

new.mv.1 <- seq(quantile(df.total.valid.12$scaledMeanValue,0.025),
                quantile(df.total.valid.12$scaledMeanValue,0.975),0.1)

eff.df.mv.12 <- marginalConflictMVEffect(model.conflict.12,
                                         df.total.valid.12$scaledMeanValue,
                                         new.mv.1) %>%
  dplyr::mutate(scaledMeanValue=x,
                catChoiceCondition='XOR - OR',
                fit=eff,
                upper=eff+ci,
                lower=eff-ci,
                se=NA,
                study='Study 12')

p.eff.cc.int.12<-ggplot(data=eff.df.mv.12, aes(x=x, y=fit)) + 
  geom_line(size=0.5)+theme_bw(12) +
  geom_ribbon(data=eff.df.mv.12, aes(x=x, max = upper, min = lower),alpha=0.3, inherit.aes = FALSE)+ 
  xlab("Overall Value\n(z-scored)") + ylab('Effect of Inclusivity') +
  theme(panel.border = element_blank(), panel.grid.major = element_blank(), plot.title = element_text(hjust = 0.5,size=6),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),axis.ticks=element_line(color='black',size=0.2),strip.text.y = element_blank()) +
  theme(legend.justification=c(1,1),legend.position='none',text = element_text(size=6)) + geom_hline(yintercept=0,color='#555555',size=0.2) + 
  scale_fill_manual("",values=c("#005555","#550055")) + scale_color_manual("",values=c("#005555","#550055")) + # ggtitle('Exclusive - Non-Exclusive') +
  coord_cartesian(ylim=c(-1.6,0.1)) + scale_y_continuous(breaks = c(-1.6,0))

p.eff.cc.int.12

# ggsave('figures/ov_conflict_123.pdf',unit='cm',width=5,height=5)

eff_vd.cfl.12 <- Effect(c("scaledValueDiff","catChoiceCondition"),
                   model.conflict.12,
                   xlevels=list(scaledValueDiff=seq(quantile(df.total.rt.12$scaledValueDiff,0.025),
                                                    quantile(df.total.rt.12$scaledValueDiff,0.975),0.1)))

## Warning in Analyze.model(focal.predictors, mod, xlevels, default.levels, : the
## predictors scaledValueDiff, scaledTrialNum, scaledMeanValue are one-column
## matrices that were converted to vectors

IA.vd.cfl <- as.data.frame(eff_vd.cfl.12) %>% dplyr::mutate(study='Study 12')


IA.vd.cfl$catChoiceCondition <- relevel(IA.vd.cfl$catChoiceCondition,ref = 'XOR')

p.eff.vd.cfl.12<-ggplot(data=IA.vd.cfl, aes(x=scaledValueDiff, y=fit,group=catChoiceCondition)) +
  geom_line(size=0.5,aes(color=catChoiceCondition))+theme_bw(12) +
  geom_ribbon(data=IA.vd.cfl, aes(x=scaledValueDiff, max = upper, min = lower,fill=catChoiceCondition),alpha=0.3, inherit.aes = FALSE)+ 
  xlab("Relative Value\n(z-scored)") + ylab("Conflict") + 
  theme(panel.border = element_blank(), panel.grid.major = element_blank(), plot.title = element_text(hjust = 0.5,size=6),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),axis.ticks = element_line(colour='black',size=0.2)) +
  theme(legend.justification=c(1,1),legend.position='none',text = element_text(size=6)) + 
  scale_fill_manual("",values=c('#0673C3','#00B024')) + 
  scale_color_manual("",values=c('#0673C3','#00B024')) + 
  coord_cartesian(ylim=c(1,4)) + scale_y_continuous(breaks = c(1,4))

p.eff.vd.cfl.12

#ggsave('Study12_RT.pdf')

lay <- rbind(c(1,NA,2,NA,3,NA,4))

plots <- list(p.diff.conflict.12,p.eff.mv.cfl.12,p.eff.cc.int.12,p.eff.vd.cfl.12)
grobs <- list()
widths <- list()
heights <- list()

for (i in 1:length(plots)){
    grobs[[i]] <- ggplotGrob(plots[[i]])
    widths[[i]] <- grobs[[i]]$widths
    heights[[i]] <- grobs[[i]]$heights
}

maxwidth <- do.call(grid::unit.pmax, widths)
maxheight <- do.call(grid::unit.pmax, heights)

for (i in 1:length(grobs)){
  grobs[[i]]$widths <- as.list(maxwidth)
  grobs[[i]]$heights <- as.list(maxheight)
}

for (i in 2:length(grobs)){
  grobs[[i]]$heights <- as.list(maxheight)
} 

p<-grid.arrange(grobs = grobs, layout_matrix = lay,widths=unit(c(2,0.1,2.7,0.1,2.7,0.1,2.7), c("cm", "cm")),heights=unit(c(3),c('cm','cm')))

ggsave(filename = '../Figures/Figure_4.pdf',p,units = 'cm',width = 25,height = 12)

model.RT.3 <- lmerTest::lmer(firstRT ~ catChoiceCondition * scaledMeanValue + catChoiceCondition * scaledValueDiff + scaledTrialNum + 
                     (1 + catChoiceCondition * scaledMeanValue + catChoiceCondition * scaledValueDiff + scaledTrialNum|participant),
                     data=df.total.rt.3,
                   control=lmerControl(optCtrl=list(maxfun=1e6)))

## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## unable to evaluate scaled gradient

## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge: degenerate Hessian with 1 negative eigenvalues

## Warning: Model failed to converge with 1 negative eigenvalue: -2.9e+02

model.RT.3.nest <- lmerTest::lmer(firstRT ~ catChoiceCondition / scaledMeanValue + catChoiceCondition / scaledValueDiff + scaledTrialNum + 
                     (1 + catChoiceCondition / scaledMeanValue + catChoiceCondition / scaledValueDiff + scaledTrialNum|participant),
                     data=df.total.rt.3,
                   control=lmerControl(optCtrl=list(maxfun=1e6)))

## boundary (singular) fit: see help('isSingular')

## Warning: Model failed to converge with 1 negative eigenvalue: -1.8e+02

model.acc.3 <- glmer(isWorstFirst ~ catChoiceCondition * scaledMeanValue + catChoiceCondition * scaledValueDiff +
                        scaledTrialNum + 
                     (1 + catChoiceCondition * scaledMeanValue + catChoiceCondition * scaledValueDiff +
                        scaledTrialNum|participant),
                     data=df.total.rt.3,family=binomial)

## boundary (singular) fit: see help('isSingular')

model.acc.3.dummy <- lmer(isWorstFirst ~ catChoiceCondition * scaledMeanValue + catChoiceCondition * scaledValueDiff +
                        scaledTrialNum + 
                     (1 + catChoiceCondition * scaledMeanValue + catChoiceCondition * scaledValueDiff +
                        scaledTrialNum|participant),
                     data=df.total.rt.3)

## boundary (singular) fit: see help('isSingular')

model.acc.3.nest <- lmer(isWorstFirst ~ catChoiceCondition / scaledMeanValue + catChoiceCondition / scaledValueDiff +
                        scaledTrialNum + 
                     (1 + catChoiceCondition / scaledMeanValue + catChoiceCondition / scaledValueDiff +
                        scaledTrialNum|participant),
                     data=df.total.rt.3)

## boundary (singular) fit: see help('isSingular')

tab_model(model.RT.3,model.acc.3,show.re.var = F,transform = NULL,pred.labels = c("Intercept","Inclusivity","Overall Value","Relative Value","Trial Order","Incl by OV","Incl by RV"),dv.labels = c("Reaction Time","Accuracy"))

	Reaction Time			Accuracy
Predictors	Estimates	CI	p	Log-Odds	CI	p
Intercept	3.04	2.90 – 3.18	<0.001	-0.25	-0.34 – -0.16	<0.001
Inclusivity	-0.13	-0.19 – -0.07	<0.001	-0.14	-0.23 – -0.06	0.001
Overall Value	0.43	0.38 – 0.47	<0.001	0.09	0.04 – 0.14	0.001
Relative Value	-0.16	-0.19 – -0.13	<0.001	0.48	0.41 – 0.55	<0.001
Trial Order	-0.16	-0.20 – -0.12	<0.001	-0.05	-0.09 – -0.01	0.023
Incl by OV	0.07	0.03 – 0.12	0.003	0.06	-0.03 – 0.15	0.165
Incl by RV	-0.01	-0.05 – 0.04	0.761	-0.08	-0.17 – 0.01	0.070
ICC	0.33			0.07
N	98 participant			98 participant
Observations	11476			11476
Marginal R2 / Conditional R2	0.117 / 0.409			0.066 / 0.133

model.conflict.3 <- lmerTest::lmer(conflict ~ catChoiceCondition * poly(scaledMeanValue,2) + catChoiceCondition * scaledValueDiff + scaledTrialNum + (1 + catChoiceCondition * poly(scaledMeanValue,2) + catChoiceCondition * scaledValueDiff + scaledTrialNum|participant),data=df.total.valid.3)

## boundary (singular) fit: see help('isSingular')

model.conflict.3.coeff <- lmerTest::lmer(conflict ~ catChoiceCondition / poly(scaledMeanValue,2) + catChoiceCondition / scaledValueDiff + scaledTrialNum + 
                     (1 + catChoiceCondition / poly(scaledMeanValue,2) + catChoiceCondition / scaledValueDiff + scaledTrialNum|participant),
                     data=df.total.valid.3)

## boundary (singular) fit: see help('isSingular')

## Warning: Model failed to converge with 1 negative eigenvalue: -1.9e+02

tab_model(model.conflict.3,transform = NULL,show.re.var = F,pred.labels = c("Intercept","Inclusivity","Overall Value","Overall Value^2","Relative Value","Trial Order","Incl by OV","Incl by OV^2","Excl by RV"),dv.labels = c("Conflict"))

	Conflict
Predictors	Estimates	CI	p
Intercept	2.21	2.12 – 2.30	<0.001
Inclusivity	-0.08	-0.15 – -0.01	0.030
Overall Value	46.04	37.12 – 54.96	<0.001
Overall Value^2	20.84	16.61 – 25.06	<0.001
Relative Value	-0.07	-0.10 – -0.03	<0.001
Trial Order	-0.00	-0.03 – 0.03	0.951
Incl by OV	7.24	1.23 – 13.25	0.018
Incl by OV^2	-2.45	-7.29 – 2.40	0.322
Excl by RV	0.03	-0.01 – 0.07	0.195
N participant	98
Observations	11760
Marginal R2 / Conditional R2	0.241 / NA

4.3.0.1 Get prediction for two ORXOR studies

coeff.rt <- t(fixef(model.RT.3)['catChoiceConditionOR-XOR'])
df.ci <- confint(model.RT.3,method="Wald")
df.ci <- df.ci[!is.na(df.ci[,1]),]
ci.rt <- df.ci['catChoiceConditionOR-XOR',]
estimate.rt <- cbind(coeff.rt,t(ci.rt))
colnames(estimate.rt)<-c('coeff','lower','upper')

coeff.acc <- t(fixef(model.acc.3.dummy)['catChoiceConditionOR-XOR'])
df.ci <- confint(model.acc.3.dummy,method="Wald")
df.ci <- df.ci[!is.na(df.ci[,1]),]
ci.acc <- df.ci['catChoiceConditionOR-XOR',]
estimate.acc <- cbind(coeff.acc,t(ci.acc))
colnames(estimate.acc)<-c('coeff','lower','upper')

coeff.conf <- t(fixef(model.conflict.3)['catChoiceConditionOR-XOR'])
df.ci <- confint(model.conflict.3,method="Wald")
df.ci <- df.ci[!is.na(df.ci[,1]),]
ci.conf <- df.ci['catChoiceConditionOR-XOR',]
estimate.conf <- cbind(coeff.conf,t(ci.conf))
colnames(estimate.conf)<-c('coeff','lower','upper')

estimate.all <- data.frame(rbind(estimate.rt,estimate.acc,estimate.conf))
estimate.all$var <- c('RT','Acc','Conflict')

p.diff.acc.3 <- ggplot(estimate.all %>% filter(var %in% c('Acc')), aes(x=var, y=coeff))  + geom_hline(yintercept=0,color='#555555',size=0.2) + 
  geom_point(stat="identity", position=position_dodge(0.6),size=0.5) +
  geom_errorbar(aes(ymin=lower, ymax=upper), width=0.1,size=0.4,
                 position=position_dodge(.6))+labs(x="", y = "Effect of Inclusivity")+theme_bw(12) + 
  theme(panel.border = element_blank(),panel.grid.major = element_blank(),
        axis.title.x = element_text(margin = margin(t = 0, r = 0, b = 0, l = 0)),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),axis.ticks = element_line(colour = "black",size=0.2),
        text=element_text(size=6),legend.position="none") +
  scale_x_discrete(labels=c("Acc"='P(Worst First)')) + scale_y_continuous(limits = c(-0.1,0.004),breaks = c(-0.1,0))
p.diff.acc.3

p.diff.rt.3 <- ggplot(estimate.all %>% filter(var %in% c('RT')), aes(x=var, y=coeff))  + geom_hline(yintercept=0,color='#555555',size=0.2) + 
  geom_point(stat="identity", position=position_dodge(0.6),size=0.5) +
  geom_errorbar(aes(ymin=lower, ymax=upper), width=0.1,size=0.4,
                 position=position_dodge(.6))+labs(x="", y = "Effect of Inclusivity")+theme_bw(12) + 
  theme(panel.border = element_blank(),panel.grid.major = element_blank(),
        axis.title.x = element_text(margin = margin(t = 0, r = 0, b = 0, l = 0)),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),axis.ticks = element_line(colour = "black",size=0.2),
        text=element_text(size=6),legend.position="none") +
  scale_x_discrete(labels=c("RT"='RT')) + 
  scale_color_manual(values=c('#0673C3','#00B024')) + scale_y_continuous(limits = c(-0.5,0.02),breaks = c(-0.5,0))
p.diff.rt.3

p.diff.conflict.3 <- ggplot(estimate.all %>% filter(var %in% c('Conflict')), aes(x=var, y=coeff))  + geom_hline(yintercept=0,color='#555555',size=0.2) + 
  geom_point(stat="identity", position=position_dodge(0.6),size=0.5) +
  geom_errorbar(aes(ymin=lower, ymax=upper), width=0.1,size=0.4,
                 position=position_dodge(.6))+labs(x="", y = "Effect of Inclusivity")+theme_bw(12) + 
  theme(panel.border = element_blank(),panel.grid.major = element_blank(),
        axis.title.x = element_text(margin = margin(t = 0, r = 0, b = 0, l = 0)),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),axis.ticks = element_line(colour = "black",size=0.2),
        text=element_text(size=6),legend.position="none") +
  scale_x_discrete(labels=c("Conflict"='Conflict')) + scale_y_continuous(limits = c(-0.5,0.02),breaks = c(-0.5,0))
p.diff.conflict.3

eff_mv.RT.3 <- Effect(c("scaledMeanValue","catChoiceCondition"),
                   model.RT.3,
                   xlevels=list(scaledMeanValue=seq(quantile(df.total.rt.3$scaledMeanValue,0.025),
                                                    quantile(df.total.rt.3$scaledMeanValue,0.975),0.1)))

## Warning in Analyze.model(focal.predictors, mod, xlevels, default.levels, : the
## predictors scaledMeanValue, scaledValueDiff, scaledTrialNum are one-column
## matrices that were converted to vectors

IA.mv.RT.3 <- as.data.frame(eff_mv.RT.3) %>% dplyr::mutate(study='Study 3')

p.eff.mv.rt.3<-ggplot(data=IA.mv.RT.3, aes(x=scaledMeanValue, y=fit, group=catChoiceCondition)) +
  geom_line(size=0.5,aes(linetype=study,color=catChoiceCondition))+theme_bw(12) +
  geom_ribbon(data=IA.mv.RT.3, aes(x=scaledMeanValue, max = upper, min = lower,fill=catChoiceCondition),alpha=0.3, inherit.aes = FALSE)+ 
  xlab("Overall Value\n(z-scored)") + ylab("RT (sec)") + 
  theme(panel.border = element_blank(), panel.grid.major = element_blank(),
        axis.title.x = element_text(margin = margin(t = 0, r = 0, b = 0, l = 0)),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),axis.ticks = element_line(colour = "black",size=0.2)) +
  theme(legend.justification=c(1,1),legend.position='none',text = element_text(size=6)) + 
  scale_fill_manual("",values=c('#0673C3','#00B024')) + 
  scale_color_manual("",values=c('#0673C3','#00B024')) + 
  coord_cartesian(ylim=c(1,4)) + scale_y_continuous(breaks = c(1,4))

p.eff.mv.rt.3

eff_vd.RT.3 <- Effect(c("scaledValueDiff","catChoiceCondition"),
                   model.RT.3,
                   xlevels=list(scaledValueDiff=seq(quantile(df.total.rt.3$scaledValueDiff,0.025),
                                                    quantile(df.total.rt.3$scaledValueDiff,0.975),0.1)))

## Warning in Analyze.model(focal.predictors, mod, xlevels, default.levels, : the
## predictors scaledMeanValue, scaledValueDiff, scaledTrialNum are one-column
## matrices that were converted to vectors

IA.vd.RT.3 <- as.data.frame(eff_vd.RT.3) %>% dplyr::mutate(study='Study 3')

p.eff.vd.rt.3<-ggplot(data=IA.vd.RT.3, aes(x=scaledValueDiff, y=fit, group=catChoiceCondition)) +
  geom_line(size=0.5,aes(linetype=study,color=catChoiceCondition))+theme_bw(12) +
  geom_ribbon(data=IA.vd.RT.3, aes(x=scaledValueDiff, max = upper, min = lower,fill=catChoiceCondition),alpha=0.3, inherit.aes = FALSE)+ 
  xlab("Relative Value\n(z-scored)") + ylab("RT (sec)") + 
  theme(panel.border = element_blank(), panel.grid.major = element_blank(),
        axis.title.x = element_text(margin = margin(t = 0, r = 0, b = 0, l = 0)),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),axis.ticks = element_line(colour = "black",size=0.2)) +
  theme(legend.justification=c(1,1),legend.position='none',text = element_text(size=6)) + 
  scale_fill_manual("",values=c('#0673C3','#00B024')) + 
  scale_color_manual("",values=c('#0673C3','#00B024')) + 
  coord_cartesian(ylim=c(1,4)) + scale_y_continuous(breaks = c(1,4))

p.eff.vd.rt.3

eff_mv.acc.3 <- Effect(c("scaledMeanValue","catChoiceCondition"),
                   model.acc.3,
                   xlevels=list(scaledMeanValue=seq(quantile(df.total.rt.3$scaledMeanValue,0.025),
                                                    quantile(df.total.rt.3$scaledMeanValue,0.972),0.1)))

## Warning in Analyze.model(focal.predictors, mod, xlevels, default.levels, : the
## predictors scaledMeanValue, scaledValueDiff, scaledTrialNum are one-column
## matrices that were converted to vectors

IA.mv.acc.3 <- as.data.frame(eff_mv.acc.3) %>% dplyr::mutate(study='Study 3')

p.eff.mv.acc.3 <-ggplot(data=IA.mv.acc.3, aes(x=scaledMeanValue, y=fit, group=catChoiceCondition)) +
  geom_line(size=0.5,aes(linetype=study,color=catChoiceCondition))+theme_bw(12) +
  geom_ribbon(data=IA.mv.acc.3, aes(x=scaledMeanValue, max = upper, min = lower,fill=catChoiceCondition),alpha=0.3, inherit.aes = FALSE)+ 
  xlab("Overall value\n(z-scored)") + ylab("P(Worst First)") + 
  theme(panel.border = element_blank(), panel.grid.major = element_blank(),
        axis.title.x = element_text(margin = margin(t = 0, r = 0, b = 0, l = 0)),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),axis.ticks = element_line(colour = "black",size=0.2)) +
  theme(legend.justification=c(1,1),legend.position='none',text = element_text(size=6)) + 
  scale_fill_manual("",values=c('#0673C3','#00B024')) + 
  scale_color_manual("",values=c('#0673C3','#00B024')) + 
  coord_cartesian(ylim=c(0.2,0.8)) + scale_y_continuous(breaks = c(0.2,0.8),labels=function(x) sprintf("%.1f", x))

p.eff.mv.acc.3

#ggsave('Study12_RT.pdf')

eff_vd.acc.3 <- Effect(c("scaledValueDiff","catChoiceCondition"),
                   model.acc.3,
                   xlevels=list(scaledValueDiff=seq(quantile(df.total.rt.3$scaledValueDiff,0.025),
                                                    quantile(df.total.rt.3$scaledValueDiff,0.975),0.1)))

## Warning in Analyze.model(focal.predictors, mod, xlevels, default.levels, : the
## predictors scaledMeanValue, scaledValueDiff, scaledTrialNum are one-column
## matrices that were converted to vectors

IA.vd.acc.3 <- as.data.frame(eff_vd.acc.3) %>% dplyr::mutate(study='Study 3')

p.eff.vd.acc.3<-ggplot(data=IA.vd.acc.3, aes(x=scaledValueDiff, y=fit, group=catChoiceCondition)) +
  geom_line(size=0.5,aes(linetype=study,color=catChoiceCondition))+theme_bw(12) +
  geom_ribbon(data=IA.vd.acc.3, aes(x=scaledValueDiff, max = upper, min = lower,fill=catChoiceCondition),alpha=0.3, inherit.aes = FALSE)+ 
  xlab("Relative Value\n(z-scored)") + ylab("P(Worst First)") + 
  theme(panel.border = element_blank(), panel.grid.major = element_blank(),
        axis.title.x = element_text(margin = margin(t = 0, r = 0, b = 0, l = 0)),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),axis.ticks = element_line(colour = "black",size=0.2)) +
  theme(legend.justification=c(1,1),legend.position='none',text = element_text(size=6)) + 
  scale_fill_manual("",values=c('#0673C3','#00B024')) + 
  scale_color_manual("",values=c('#0673C3','#00B024')) + 
  coord_cartesian(ylim=c(0.2,0.8)) + scale_y_continuous(breaks = c(0.2,0.8),labels=function(x) sprintf("%.1f", x))

p.eff.vd.acc.3

#ggsave('Study12_RT.pdf')

eff_mv.cfl.3 <- Effect(c("scaledMeanValue","catChoiceCondition"),
                       model.conflict.3,
                       xlevels=list(scaledMeanValue=seq(quantile(df.total.valid.3$scaledMeanValue,0.025),
                                                        quantile(df.total.valid.3$scaledMeanValue,0.975),0.1)))

## Warning in Analyze.model(focal.predictors, mod, xlevels, default.levels, : the
## predictors scaledValueDiff, scaledTrialNum, scaledMeanValue are one-column
## matrices that were converted to vectors

IA.mv.cfl.3 <- as.data.frame(eff_mv.cfl.3) %>% dplyr::mutate(study='Study 3')

IA.mv.cfl <- IA.mv.cfl.3

IA.mv.cfl$catChoiceCondition <- relevel(IA.mv.cfl$catChoiceCondition,ref = 'XOR')

p.eff.mv.cfl.3<-ggplot(data=IA.mv.cfl, aes(x=scaledMeanValue, y=fit,group=catChoiceCondition)) +
  geom_line(size=0.5,aes(linetype=study,color=catChoiceCondition))+theme_bw(12) +
  geom_ribbon(data=IA.mv.cfl, aes(x=scaledMeanValue, max = upper, min = lower,fill=catChoiceCondition),alpha=0.3, inherit.aes = FALSE)+ 
  xlab("Overall value\n(z-scored)") + ylab("Conflict") + 
  theme(panel.border = element_blank(), panel.grid.major = element_blank(),
        axis.title.x = element_text(margin = margin(t = 0, r = 0, b = 0, l = 0)),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),axis.ticks = element_line(colour = "black",size=0.2)) +
  theme(legend.justification=c(1,1),legend.position='none',text = element_text(size=6)) + 
  scale_fill_manual("",values=c('#0673C3','#00B024')) + 
  scale_color_manual("",values=c('#0673C3','#00B024')) + # ggtitle('Exclusive') +
  coord_cartesian(ylim=c(1,4)) + scale_y_continuous(breaks = c(1,4))

p.eff.mv.cfl.3

# ggsave('figures/ov_conflict_by_cond_d.pdf',width=4,height=2.5)

new.mv.1 <- seq(quantile(df.total.valid.3$scaledMeanValue,0.025),
                quantile(df.total.valid.3$scaledMeanValue,0.975),0.1)

eff.df.mv.3 <- marginalConflictMVEffect(model.conflict.3,df.total.valid.3$scaledMeanValue,new.mv.1) %>%
  dplyr::mutate(scaledMeanValue=x,
                catChoiceCondition='XOR - OR',
                fit= eff,
                upper= eff+ci,
                lower= eff-ci,
                se=NA,
                study='Study 3')

p.eff.cc.int.3<-ggplot(data=eff.df.mv.3, aes(x=x, y=fit)) + 
  geom_line(size=0.5)+theme_bw(12) +
  geom_ribbon(data=eff.df.mv.3, aes(x=x, max = upper, min = lower),alpha=0.3, inherit.aes = FALSE)+ 
  xlab("Overall value\n(z-scored)") + ylab('Effect of Inclusivity') +
  theme(panel.border = element_blank(), panel.grid.major = element_blank(),
        axis.title.x = element_text(margin = margin(t = 0, r = 0, b = 0, l = 0)),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),axis.ticks = element_line(colour = "black",size=0.2)) +
  theme(legend.justification=c(1,1),legend.position='none',text = element_text(size=6)) + geom_hline(yintercept=0,color='#555555') + 
  scale_fill_manual("",values=c("#005555","#550055")) + scale_color_manual("",values=c("#005555","#550055")) + # ggtitle('Exclusive - Non-Exclusive') +
  coord_cartesian(ylim=c(-0.8,0.2)) + scale_y_continuous(breaks = c(-0.8,0))

p.eff.cc.int.3

eff_vd.cfl.3 <- Effect(c("scaledValueDiff","catChoiceCondition"),
                   model.conflict.3,
                   xlevels=list(scaledValueDiff=seq(quantile(df.total.rt.3$scaledValueDiff,0.025),
                                                    quantile(df.total.rt.3$scaledValueDiff,0.975),0.1)))

## Warning in Analyze.model(focal.predictors, mod, xlevels, default.levels, : the
## predictors scaledValueDiff, scaledTrialNum, scaledMeanValue are one-column
## matrices that were converted to vectors

IA.vd.cfl <- as.data.frame(eff_vd.cfl.3) %>% dplyr::mutate(study='Study 1')

IA.vd.cfl$catChoiceCondition <- relevel(IA.vd.cfl$catChoiceCondition,ref = 'XOR')

p.eff.vd.cfl.3<-ggplot(data=IA.vd.cfl, aes(x=scaledValueDiff, y=fit,group=catChoiceCondition)) +
  geom_line(size=0.5,aes(color=catChoiceCondition))+theme_bw(12) +
  geom_ribbon(data=IA.vd.cfl, aes(x=scaledValueDiff, max = upper, min = lower,fill=catChoiceCondition),alpha=0.3, inherit.aes = FALSE)+ 
  xlab("Relative Value\n(z-scored)") + ylab("Conflict") + 
  theme(panel.border = element_blank(), panel.grid.major = element_blank(),
        axis.title.x = element_text(margin = margin(t = 0, r = 0, b = 0, l = 0)),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),axis.ticks = element_line(colour = "black",size=0.2)) +
  theme(legend.justification=c(1,1),legend.position='none',text = element_text(size=6)) + 
  scale_fill_manual("",values=c('#0673C3','#00B024')) + 
  scale_color_manual("",values=c('#0673C3','#00B024')) + 
  coord_cartesian(ylim=c(1,4)) + scale_y_continuous(breaks = c(1,4))

p.eff.vd.cfl.3

#ggsave('Study12_RT.pdf')

lay <- rbind(c(1,NA,2,NA,NA,3,3,NA),
             c(4,NA,5,NA,NA,6,6,NA),
             c(7,NA,8,NA,9,9,10,10))

plots <- list(p.diff.rt.3,p.eff.vd.rt.3,p.eff.mv.rt.3,
              p.diff.acc.3,p.eff.vd.acc.3,p.eff.mv.acc.3,
              p.diff.conflict.3,p.eff.vd.cfl.3,p.eff.mv.cfl.3,p.eff.cc.int.3)
grobs <- list()
widths <- list()
heights <- list()

for (i in 1:length(plots)){
    grobs[[i]] <- ggplotGrob(plots[[i]])
    widths[[i]] <- grobs[[i]]$widths
    heights[[i]] <- grobs[[i]]$heights
}

maxwidth <- do.call(grid::unit.pmax, widths)
maxheight <- do.call(grid::unit.pmax,heights)

for (i in 1:length(grobs)){
     grobs[[i]]$heights <- as.list(maxheight)
     grobs[[i]]$widths <- as.list(maxwidth)
}


for (i in 1:length(grobs)){
     grobs[[i]]$heights <- as.list(maxheight)
     grobs[[i]]$widths <- as.list(maxwidth)
}


p<-grid.arrange(grobs = grobs, layout_matrix = lay,widths=unit(c(2,0.1,2.7,0.1,0.8,1.35,1.35,0.8), c("cm", "cm")),heights=unit(c(3,3,3),c('cm','cm')))

ggsave(filename = '../Figures/Figure5_V3.pdf',p,units = 'cm',width = 25,height = 20)

df.total.rt.3$scaledRT<-scale(df.total.rt.3$firstRT)

model.conflict.3.rt <- lmerTest::lmer(conflict ~ scaledRT + acc + catChoiceCondition * poly(scaledMeanValue,2) + catChoiceCondition * scaledValueDiff + scaledTrialNum + (1 + scaledRT + acc + catChoiceCondition * poly(scaledMeanValue,2) + catChoiceCondition * scaledValueDiff + scaledTrialNum|participant), data=df.total.rt.3)

## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 0.0748015 (tol = 0.002, component 1)

## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: large eigenvalue ratio
##  - Rescale variables?

tab_model(model.conflict.3.rt,show.re.var = FALSE,pred.labels = c('Intercept','RT','Accuracy','Inclusivity','OV','OV^2','RV','Trial Num','Incl by OV','Incl by OV^2','Excl by RV'))

	conflict
Predictors	Estimates	CI	p
Intercept	2.20	2.10 – 2.30	<0.001
RT	0.13	0.09 – 0.16	<0.001
Accuracy	0.07	0.01 – 0.13	0.014
Inclusivity	-0.08	-0.15 – -0.01	0.029
OV	39.80	31.56 – 48.03	<0.001
OV^2	18.80	14.79 – 22.82	<0.001
RV	-0.05	-0.07 – -0.02	0.001
Trial Num	0.01	-0.03 – 0.04	0.692
Incl by OV	4.43	-1.55 – 10.40	0.147
Incl by OV^2	-3.50	-8.19 – 1.20	0.144
Excl by RV	0.03	-0.01 – 0.07	0.187
ICC	0.40
N participant	98
Observations	11476
Marginal R2 / Conditional R2	0.161 / 0.494

df.rating.new.s <- read.csv('../Data/Study3/Selection/Study3a_2.csv')

df.total.new.s <- read.csv('../Data/Study3/Selection/Study3a_1.csv') %>%
  mutate(catChoiceCondition=relevel(factor(catChoiceCondition),ref = 'XOR'),
         isBestFirst=firstValue==bestValue,
         scaledTrialNum=scale(trialN),
         scaledMeanValue=scale(meanValue),
         scaledValueDiff=scale(valueDiff))

df.total.rt.new.s <- df.total.new.s %>% filter(firstRT>0.1,firstRT<18) %>%
  mutate(scaledMeanValue=scale(meanValue),
         scaledValueDiff=scale(valueDiff),
         scaledTrialNum=scale(trialN))

contrasts(df.total.new.s$catChoiceCondition) <- contr.sdif
contrasts(df.total.rt.new.s$catChoiceCondition) <- contr.sdif

df.or.rt.new.s <- df.total.rt.new.s %>% filter(catChoiceCondition=='OR',NChosen>=1) %>%
    dplyr::mutate(scaledMeanValue=scale(meanValue),
                  scaledValueDiff=scale(valueDiff),
                  scaledTrialNum=scale(trialN),
                  scaledFirstRT=scale(firstRT),
                  acc=factor(isBestFirst))

contrasts(df.or.rt.new.s$acc)<-contr.sum

df.rating.new.d <- read.csv('../Data/Study3/Removal/Study3b_2.csv')

df.total.new.d <- read.csv('../Data/Study3/Removal/Study3b_1.csv') %>%
  mutate(catChoiceCondition=relevel(factor(catChoiceCondition),ref = 'XOR'),
         isWorstFirst=firstValue==worstValue,
         scaledTrialNum=scale(trialN),
         scaledMeanValue=scale(meanValue),
         scaledValueDiff=scale(valueDiff))

df.total.rt.new.d <- df.total.new.d %>% filter(firstRT>0.1,firstRT<18) %>%
  mutate(scaledMeanValue=scale(meanValue),
         scaledValueDiff=scale(valueDiff),
         scaledTrialNum=scale(trialN))


contrasts(df.total.new.d$catChoiceCondition) <- contr.sdif
contrasts(df.total.rt.new.d$catChoiceCondition) <- contr.sdif

df.or.rt.new.d <- df.total.rt.new.d %>% filter(catChoiceCondition=='OR',NChosen>=1) %>%
    dplyr::mutate(scaledMeanValue=scale(meanValue),
                  scaledValueDiff=scale(valueDiff),
                  scaledTrialNum=scale(trialN),
                  scaledFirstRT=scale(firstRT),
                  acc=factor(isWorstFirst))

contrasts(df.or.rt.new.d$acc)<-contr.sum

model.RT.ns <-  lmerTest::lmer(log10(firstRT) ~ catChoiceCondition * scaledMeanValue + catChoiceCondition * scaledValueDiff + scaledTrialNum + (1 + catChoiceCondition * scaledMeanValue + catChoiceCondition * scaledValueDiff + scaledTrialNum|participant),data=df.total.rt.new.s)

## boundary (singular) fit: see help('isSingular')

model.RT.ns.r <-  lmerTest::lmer(firstRT ~ catChoiceCondition * scaledMeanValue + catChoiceCondition * scaledValueDiff + scaledTrialNum + (1 + catChoiceCondition * scaledMeanValue + catChoiceCondition * scaledValueDiff + scaledTrialNum|participant),data=df.total.rt.new.s)

## boundary (singular) fit: see help('isSingular')

model.acc.ns <- glmer(isBestFirst ~ catChoiceCondition * scaledMeanValue +  catChoiceCondition * scaledValueDiff + scaledTrialNum + (1 + catChoiceCondition * scaledMeanValue +  catChoiceCondition * scaledValueDiff + scaledTrialNum|participant),data=df.total.rt.new.s,family = binomial)

## boundary (singular) fit: see help('isSingular')

model.acc.ns.dummy <- lmerTest::lmer(isBestFirst ~ catChoiceCondition * scaledMeanValue +  catChoiceCondition * scaledValueDiff + scaledTrialNum + (1 + catChoiceCondition * scaledMeanValue +  catChoiceCondition * scaledValueDiff + scaledTrialNum|participant),data=df.total.rt.new.s)

## boundary (singular) fit: see help('isSingular')

## Warning: Model failed to converge with 1 negative eigenvalue: -4.7e-01

model.rating.ns <- lmerTest::lmer(conflict ~ catChoiceCondition * poly(scaledMeanValue,2) + catChoiceCondition * scaledValueDiff + scaledTrialNum + (1 + catChoiceCondition * poly(scaledMeanValue,2) + catChoiceCondition * scaledValueDiff + scaledTrialNum|participant),data=df.total.new.s)

## boundary (singular) fit: see help('isSingular')

## Warning: Model failed to converge with 1 negative eigenvalue: -1.2e-02

tab_model(model.RT.ns,model.acc.ns,model.rating.ns,show.re.var = FALSE,transform = NULL,digits=3)

	log10(firstRT)			isBestFirst			conflict
Predictors	Estimates	CI	p	Log-Odds	CI	p	Estimates	CI	p
(Intercept)	0.460	0.422 – 0.497	<0.001	-0.066	-0.174 – 0.043	0.235	2.469	2.320 – 2.617	<0.001
catChoiceConditionOR-XOR	-0.017	-0.030 – -0.004	0.013	0.001	-0.103 – 0.105	0.983	-0.332	-0.488 – -0.176	<0.001
scaledMeanValue	-0.061	-0.070 – -0.052	<0.001	0.078	0.014 – 0.141	0.016
scaledValueDiff	-0.032	-0.039 – -0.025	<0.001	0.603	0.520 – 0.686	<0.001	-0.089	-0.132 – -0.046	<0.001
scaledTrialNum	-0.035	-0.045 – -0.025	<0.001	-0.037	-0.093 – 0.018	0.191	0.001	-0.038 – 0.040	0.967
catChoiceConditionOR-XOR × scaledMeanValue	-0.017	-0.028 – -0.007	0.001	0.031	-0.082 – 0.144	0.590
catChoiceConditionOR-XOR × scaledValueDiff	-0.004	-0.013 – 0.005	0.391	-0.117	-0.241 – 0.008	0.066	-0.003	-0.066 – 0.060	0.930
scaledMeanValue [1st degree]							-2.857	-16.168 – 10.454	0.674
scaledMeanValue [2nd degree]							13.391	8.113 – 18.670	<0.001
catChoiceConditionOR-XOR × scaledMeanValue [1st degree]							-13.923	-22.255 – -5.592	0.001
catChoiceConditionOR-XOR × scaledMeanValue [2nd degree]							-3.965	-10.023 – 2.093	0.200
ICC	0.44
N	59 participant			59 participant			59 participant
Observations	7045			7045			7080
Marginal R2 / Conditional R2	0.089 / 0.490			0.098 / NA			0.083 / NA

model.RT.nd <- lmerTest::lmer(log10(firstRT) ~ catChoiceCondition * scaledMeanValue + catChoiceCondition * scaledValueDiff + scaledTrialNum + (1 + catChoiceCondition * scaledMeanValue + catChoiceCondition * scaledValueDiff + scaledTrialNum|participant),data=df.total.rt.new.d)

## boundary (singular) fit: see help('isSingular')

model.RT.nd.r <- lmerTest::lmer(firstRT ~ catChoiceCondition * scaledMeanValue + catChoiceCondition * scaledValueDiff + scaledTrialNum + (1 + catChoiceCondition * scaledMeanValue + catChoiceCondition * scaledValueDiff + scaledTrialNum|participant),data=df.total.rt.new.d)

## boundary (singular) fit: see help('isSingular')

model.acc.nd <- glmer(isWorstFirst ~ catChoiceCondition * scaledMeanValue +  catChoiceCondition * scaledValueDiff + scaledTrialNum + (1 + catChoiceCondition * scaledMeanValue +  catChoiceCondition * scaledValueDiff + scaledTrialNum|participant),data=df.total.rt.new.d,family = binomial)

## boundary (singular) fit: see help('isSingular')

model.acc.nd.dummy <- lmerTest::lmer(isWorstFirst ~ catChoiceCondition * scaledMeanValue +  catChoiceCondition * scaledValueDiff + scaledTrialNum + (1 + catChoiceCondition * scaledMeanValue +  catChoiceCondition * scaledValueDiff + scaledTrialNum|participant),data=df.total.rt.new.d)

## boundary (singular) fit: see help('isSingular')

model.rating.nd <- lmerTest::lmer(conflict ~ catChoiceCondition * poly(scaledMeanValue,2) + catChoiceCondition * scaledValueDiff + scaledTrialNum + (1 + catChoiceCondition *  poly(scaledMeanValue,2) + catChoiceCondition * scaledValueDiff + scaledTrialNum|participant),data=df.total.new.d)

## boundary (singular) fit: see help('isSingular')

tab_model(model.RT.nd,model.acc.nd,model.rating.nd,show.re.var = FALSE,transform = NULL)

	log10(firstRT)			isWorstFirst			conflict
Predictors	Estimates	CI	p	Log-Odds	CI	p	Estimates	CI	p
(Intercept)	0.45	0.41 – 0.49	<0.001	-0.06	-0.16 – 0.05	0.299	2.34	2.21 – 2.47	<0.001
catChoiceConditionOR-XOR	-0.01	-0.03 – -0.00	0.013	-0.05	-0.16 – 0.05	0.324	-0.08	-0.18 – 0.03	0.174
scaledMeanValue	0.07	0.06 – 0.08	<0.001	0.09	0.01 – 0.16	0.031
scaledValueDiff	-0.03	-0.03 – -0.02	<0.001	0.62	0.54 – 0.70	<0.001	-0.08	-0.12 – -0.04	<0.001
scaledTrialNum	-0.03	-0.04 – -0.02	<0.001	-0.01	-0.06 – 0.04	0.617	0.00	-0.03 – 0.03	0.965
catChoiceConditionOR-XOR × scaledMeanValue	0.02	0.01 – 0.03	<0.001	0.10	-0.01 – 0.22	0.069
catChoiceConditionOR-XOR × scaledValueDiff	-0.00	-0.01 – 0.01	0.738	0.04	-0.09 – 0.16	0.563	-0.02	-0.07 – 0.03	0.360
scaledMeanValue [1st degree]							50.71	42.68 – 58.73	<0.001
scaledMeanValue [2nd degree]							16.24	11.89 – 20.60	<0.001
catChoiceConditionOR-XOR × scaledMeanValue [1st degree]							5.98	1.32 – 10.64	0.012
catChoiceConditionOR-XOR × scaledMeanValue [2nd degree]							0.15	-4.88 – 5.19	0.952
ICC				0.07
N	61 participant			61 participant			61 participant
Observations	7279			7279			7320
Marginal R2 / Conditional R2	0.168 / NA			0.100 / 0.160			0.357 / NA

tab_model(model.RT.ns.r,model.RT.nd.r,pred.labels = c("Intercept","Inclusivity","Overall Value","Relative Value","Trial Order","Incl by OV","Incl by RV"),dv.labels = c("Replication Study-Selection RT","Replication Study-Removal RT"),show.re.var = F,show.icc = F,show.r2 = F,show.ngroups = F,show.obs = F)

	Replication Study-Selection RT			Replication Study-Removal RT
Predictors	Estimates	CI	p	Estimates	CI	p
Intercept	3.38	3.09 – 3.68	<0.001	3.34	3.08 – 3.61	<0.001
Inclusivity	-0.14	-0.25 – -0.03	0.010	-0.10	-0.20 – -0.00	0.044
Overall Value	-0.49	-0.59 – -0.39	<0.001	0.51	0.44 – 0.58	<0.001
Relative Value	-0.28	-0.35 – -0.21	<0.001	-0.26	-0.32 – -0.20	<0.001
Trial Order	-0.25	-0.32 – -0.19	<0.001	-0.25	-0.31 – -0.18	<0.001
Incl by OV	-0.15	-0.25 – -0.05	0.004	0.13	0.04 – 0.23	0.005
Incl by RV	-0.02	-0.10 – 0.07	0.723	-0.02	-0.10 – 0.07	0.709

tab_model(model.RT.ns,model.RT.nd,pred.labels = c("Intercept","Inclusivity","Overall Value","Relative Value","Trial Order","Incl by OV","Incl by RV"),dv.labels = c("Replication Study-Selection log(RT)","Replication Study-Removal log(RT)"),show.re.var = F,show.icc = F,show.r2 = F,show.ngroups = F,show.obs = F)

	Replication Study-Selection log(RT)			Replication Study-Removal log(RT)
Predictors	Estimates	CI	p	Estimates	CI	p
Intercept	0.46	0.42 – 0.50	<0.001	0.45	0.41 – 0.49	<0.001
Inclusivity	-0.02	-0.03 – -0.00	0.013	-0.01	-0.03 – -0.00	0.013
Overall Value	-0.06	-0.07 – -0.05	<0.001	0.07	0.06 – 0.08	<0.001
Relative Value	-0.03	-0.04 – -0.03	<0.001	-0.03	-0.03 – -0.02	<0.001
Trial Order	-0.03	-0.04 – -0.02	<0.001	-0.03	-0.04 – -0.02	<0.001
Incl by OV	-0.02	-0.03 – -0.01	0.001	0.02	0.01 – 0.03	<0.001
Incl by RV	-0.00	-0.01 – 0.01	0.391	-0.00	-0.01 – 0.01	0.738

coeff.rt.ns <- fixef(model.RT.ns)[c('catChoiceConditionOR-XOR','catChoiceConditionOR-XOR:scaledMeanValue','catChoiceConditionOR-XOR:scaledValueDiff')]
df.ci <- confint(model.RT.ns,method="Wald")
df.ci <- df.ci[!is.na(df.ci[,1]),]
ci.rt <- df.ci[c('catChoiceConditionOR-XOR','catChoiceConditionOR-XOR:scaledMeanValue','catChoiceConditionOR-XOR:scaledValueDiff'),]
estimate.rt.ns <- t(rbind(coeff.rt.ns,t(ci.rt)))
colnames(estimate.rt.ns)<-c('coeff','lower','upper')
rownames(estimate.rt.ns) <- NULL
estimate.rt.ns <- data.frame(estimate.rt.ns)
estimate.rt.ns$params <- c('Incl - Excl','(Incl - Excl) X OV','(Incl - Excl) X RV')
estimate.rt.ns$dv <- 'RT'

coeff.acc.ns <- fixef(model.acc.ns)[c('catChoiceConditionOR-XOR','catChoiceConditionOR-XOR:scaledMeanValue','catChoiceConditionOR-XOR:scaledValueDiff')]
df.ci <- confint(model.acc.ns,method="Wald")
df.ci <- df.ci[!is.na(df.ci[,1]),]
ci.acc <- df.ci[c('catChoiceConditionOR-XOR','catChoiceConditionOR-XOR:scaledMeanValue','catChoiceConditionOR-XOR:scaledValueDiff'),]
estimate.acc.ns <- t(rbind(coeff.acc.ns,t(ci.acc)))
colnames(estimate.acc.ns)<-c('coeff','lower','upper')
rownames(estimate.acc.ns) <- NULL
estimate.acc.ns <- data.frame(estimate.acc.ns)
estimate.acc.ns$params <- c('Incl - Excl','(Incl - Excl) X OV','(Incl - Excl) X RV')
estimate.acc.ns$dv <- 'P(Best First)'

estimate.rt.acc.ns <- rbind(estimate.rt.ns,estimate.acc.ns)
estimate.rt.acc.ns$order <- seq(1,6)
estimate.rt.acc.ns$study <- 'Selection'

coeff.rt.nd <- fixef(model.RT.nd)[c('catChoiceConditionOR-XOR','catChoiceConditionOR-XOR:scaledMeanValue','catChoiceConditionOR-XOR:scaledValueDiff')]
df.ci <- confint(model.RT.nd,method="Wald")
df.ci <- df.ci[!is.na(df.ci[,1]),]
ci.rt <- df.ci[c('catChoiceConditionOR-XOR','catChoiceConditionOR-XOR:scaledMeanValue','catChoiceConditionOR-XOR:scaledValueDiff'),]
estimate.rt.nd <- t(rbind(coeff.rt.nd,t(ci.rt)))
colnames(estimate.rt.nd)<-c('coeff','lower','upper')
rownames(estimate.rt.nd) <- NULL
estimate.rt.nd <- data.frame(estimate.rt.nd)
estimate.rt.nd$params <- c('Incl - Excl','(Incl - Excl) X OV','(Incl - Excl) X RV')
estimate.rt.nd$dv <- 'RT'

coeff.acc.nd <- fixef(model.acc.nd)[c('catChoiceConditionOR-XOR','catChoiceConditionOR-XOR:scaledMeanValue','catChoiceConditionOR-XOR:scaledValueDiff')]
df.ci <- confint(model.acc.nd,method="Wald")
df.ci <- df.ci[!is.na(df.ci[,1]),]
ci.acc <- df.ci[c('catChoiceConditionOR-XOR','catChoiceConditionOR-XOR:scaledMeanValue','catChoiceConditionOR-XOR:scaledValueDiff'),]
estimate.acc.nd <- t(rbind(coeff.acc.nd,t(ci.acc)))
colnames(estimate.acc.nd)<-c('coeff','lower','upper')
rownames(estimate.acc.nd) <- NULL
estimate.acc.nd <- data.frame(estimate.acc.nd)
estimate.acc.nd$params <- c('Incl - Excl','(Incl - Excl) X OV','(Incl - Excl) X RV')
estimate.acc.nd$dv <- 'P(Best First)'

estimate.rt.acc.nd <- rbind(estimate.rt.nd,estimate.acc.nd)
estimate.rt.acc.nd$order <- seq(1,6)
estimate.rt.acc.nd$study <- 'Deselection'

estimate.rt.acc.new <- rbind(estimate.rt.acc.ns,estimate.rt.acc.nd)
estimate.rt.acc.new$params <- factor(estimate.rt.acc.new$params,
                                     levels = c('(Incl - Excl) X RV','(Incl - Excl) X OV','Incl - Excl'))

p.summary.new.acc <- ggplot(estimate.rt.acc.new %>% filter(dv=='P(Best First)'),aes(x=params,y=coeff,group=study,color=study)) + geom_hline(yintercept=0,color='#AAAAAA',size=0.2) + geom_point(position = position_dodge(0.6),size=0.5,aes(shape=study)) + geom_errorbar(position = position_dodge(0.6),aes(ymin=lower,ymax=upper),width=0.2) + coord_flip() + theme_bw(12) + 
  theme(panel.border = element_blank(),panel.grid.major = element_blank(),
        axis.title.x = element_text(margin = margin(t = 0, r = 0, b = 0, l = 0)),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),
        axis.ticks = element_line(colour = "black",size=0.2),
        text=element_text(size=6),legend.position="none") + scale_y_continuous(limits = c(-0.5,0.5),breaks = c(-0.5,0,0.5)) +  scale_color_manual("",values=c('#222222','#AA0000')) + xlab('') + ylab('') + scale_x_discrete(labels=c('Incl - Excl'='On intercept',
                                                                                                                                                                                                                                          '(Incl - Excl) X OV'='On overall value effect','(Incl - Excl) X RV'='On relative value effect'))

p.summary.new.acc

p.summary.new.rt <- ggplot(estimate.rt.acc.new %>% filter(dv=='RT'),aes(x=params,y=coeff,group=study,color=study)) + geom_hline(yintercept=0,color='#AAAAAA',size=0.2) + geom_point(position = position_dodge(0.6),size=1,aes(shape=study)) + geom_errorbar(position = position_dodge(0.6),aes(ymin=lower,ymax=upper),width=0.2,linewidth=0.5) + coord_flip() + theme_bw(12) + 
  theme(panel.border = element_blank(),panel.grid.major = element_blank(),
        axis.title.x = element_text(margin = margin(t = 0, r = 0, b = 0, l = 0)),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),
        axis.ticks = element_line(colour = "black",size=0.2),
        text=element_text(size=6),legend.position="none") + scale_y_continuous(limits = c(-0.04,0.04),breaks = c(-0.04,0,0.04)) + scale_color_manual("",values=c('#AA0000','#222222')) + xlab('') + ylab('') + scale_x_discrete(labels=c('Incl - Excl'='On intercept',
                                                                                                                                                                                                                                          '(Incl - Excl) X OV'='On overall value effect','(Incl - Excl) X RV'='On relative value effect'))
p.summary.new.rt

ggsave(filename = '../Figures/Figure7A.pdf',p.summary.new.rt,units = 'cm',width = 5,height = 3)

new.mv.1 <- seq(min(quantile(df.total.rt.new.s$scaledMeanValue,0.025),
                    quantile(df.total.rt.new.d$scaledMeanValue,0.025)),
                max(quantile(df.total.rt.new.s$scaledMeanValue,0.975),
                    quantile(df.total.rt.new.d$scaledMeanValue,0.975)),0.1)

eff.df.mv.ns <- marginalConflictMVEffect(model.rating.ns,df.total.rt.new.s$scaledMeanValue,new.mv.1) %>%
  dplyr::mutate(scaledMeanValue=x,
                catChoiceCondition='XOR - OR',
                fit=eff,
                upper=eff+ci,
                lower=eff-ci,
                se=NA,
                study='Selection')

eff.df.mv.nd <- marginalConflictMVEffect(model.rating.nd,df.total.rt.new.d$scaledMeanValue,new.mv.1) %>%
  dplyr::mutate(scaledMeanValue=x,
                catChoiceCondition='XOR - OR',
                fit=eff,
                upper=eff+ci,
                lower=eff-ci,
                se=NA,
                study='Deselection')


eff.df.mv.new <- rbind(eff.df.mv.ns,eff.df.mv.nd)

p.eff.cc.int.new<-ggplot(data=eff.df.mv.new, aes(x=x, y=fit,group=study)) + geom_hline(yintercept=0,color='#AAAAAA',size=0.2) + 
  geom_line(size=0.5,aes(color=study))+theme_bw(12) +
  geom_ribbon(aes(x=x, max = upper, min = lower,fill=study),alpha=0.3)+ 
  xlab("Overall value\n(z-scored)") + ylab('Effect of Inclusivity') +
  theme(panel.border = element_blank(), panel.grid.major = element_blank(), plot.title = element_text(hjust = 0.5,size=6),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),
        axis.ticks = element_line(colour = "black",size=0.2),strip.text.y = element_blank()) +
  theme(legend.justification=c(1,1),legend.position='none',text = element_text(size=6)) + 
  scale_fill_manual("",values=c("#AA0000","#222222")) + scale_color_manual("",values=c("#AA0000","#222222")) + # ggtitle('Exclusive - Non-Exclusive') +
  coord_cartesian(ylim=c(-1,0.2)) + scale_y_continuous(breaks = c(-1,0))

p.eff.cc.int.new

ggsave(filename = '../Figures/Figure7B.pdf',p.eff.cc.int.new,units = 'cm',width = 3,height = 3)

coeff.rt <- t(fixef(model.RT.ns)['catChoiceConditionOR-XOR'])
df.ci <- confint(model.RT.ns,method="Wald")
df.ci <- df.ci[!is.na(df.ci[,1]),]
ci.rt <- df.ci['catChoiceConditionOR-XOR',]
estimate.rt <- cbind(coeff.rt,t(ci.rt))
colnames(estimate.rt)<-c('coeff','lower','upper')

coeff.acc <- t(fixef(model.acc.ns.dummy)['catChoiceConditionOR-XOR'])
df.ci <- confint(model.acc.ns.dummy,method="Wald")
df.ci <- df.ci[!is.na(df.ci[,1]),]
ci.acc <- df.ci['catChoiceConditionOR-XOR',]
estimate.acc <- cbind(coeff.acc,t(ci.acc))
colnames(estimate.acc)<-c('coeff','lower','upper')

coeff.conf <- t(fixef(model.rating.ns)['catChoiceConditionOR-XOR'])
df.ci <- confint(model.rating.ns,method="Wald")
df.ci <- df.ci[!is.na(df.ci[,1]),]
ci.conf <- df.ci['catChoiceConditionOR-XOR',]
estimate.conf <- cbind(coeff.conf,t(ci.conf))
colnames(estimate.conf)<-c('coeff','lower','upper')

estimate.all <- data.frame(rbind(estimate.rt,estimate.acc,estimate.conf))
estimate.all$var <- c('RT','Acc','Conflict')

p.diff.acc.ns <- ggplot(estimate.all %>% filter(var %in% c('Acc')), aes(x=var, y=coeff))  + geom_hline(yintercept=0,color='#555555',size=0.2) + 
  geom_point(stat="identity", position=position_dodge(0.6),size=0.5) +
  geom_errorbar(aes(ymin=lower, ymax=upper), width=0.1,size=0.4,
                 position=position_dodge(.6))+labs(x="", y = "Effect of Inclusivity")+theme_bw(12) + 
  theme(panel.border = element_blank(),panel.grid.major = element_blank(),
        axis.title.x = element_text(margin = margin(t = 0, r = 0, b = 0, l = 0)),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),
        axis.ticks = element_line(colour = "black",size=0.2),
        text=element_text(size=6),legend.position="none") +
  scale_x_discrete(labels=c("Acc"='P(Best First)')) + scale_y_continuous(limits = c(-0.05,0.05),breaks = c(-0.05,0.05))

p.diff.acc.ns

p.diff.rt.ns <- ggplot(estimate.all %>% filter(var %in% c('RT')), aes(x=var, y=coeff))  + geom_hline(yintercept=0,color='#555555',size=0.2) + 
  geom_point(stat="identity", position=position_dodge(0.6),size=0.5) +
  geom_errorbar(aes(ymin=lower, ymax=upper), width=0.1,size=0.4,
                 position=position_dodge(.6))+labs(x="", y = "Effect of Inclusivity")+theme_bw(12) + 
  theme(panel.border = element_blank(),panel.grid.major = element_blank(),
        axis.title.x = element_text(margin = margin(t = 0, r = 0, b = 0, l = 0)),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),
        axis.ticks = element_line(colour = "black",size=0.2),
        text=element_text(size=6),legend.position="none") +
  scale_x_discrete(labels=c("RT"='log(RT)')) + scale_y_continuous(limits = c(-0.05,0.005),breaks = c(-0.05,0))

p.diff.rt.ns

p.diff.conflict.ns <- ggplot(estimate.all %>% filter(var %in% c('Conflict')), aes(x=var, y=coeff))  + geom_hline(yintercept=0,color='#555555',size=0.2) + 
  geom_point(stat="identity", position=position_dodge(0.6),size=0.5) +
  geom_errorbar(aes(ymin=lower, ymax=upper), width=0.1,size=0.4,
                 position=position_dodge(.6))+labs(x="", y = "Effect of Inclusivity")+theme_bw(12) + 
  theme(panel.border = element_blank(),panel.grid.major = element_blank(),
        axis.title.x = element_text(margin = margin(t = 0, r = 0, b = 0, l = 0)),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),
        axis.ticks = element_line(colour = "black",size=0.2),
        text=element_text(size=6),legend.position="none") +
  scale_x_discrete(labels=c("Conflict"='Conflict')) + scale_y_continuous(limits = c(-0.5,0.02),breaks = c(-0.5,0))
p.diff.conflict.ns

eff_mv.RT.ns <- Effect(c("scaledMeanValue","catChoiceCondition"),
                   model.RT.ns,
                   xlevels=list(scaledMeanValue=seq(quantile(df.total.rt.new.s$scaledMeanValue,0.025),
                                                    quantile(df.total.rt.new.s$scaledMeanValue,0.975),0.1)))

## Warning in Analyze.model(focal.predictors, mod, xlevels, default.levels, : the
## predictors scaledMeanValue, scaledValueDiff, scaledTrialNum are one-column
## matrices that were converted to vectors

IA.mv.RT.ns <- as.data.frame(eff_mv.RT.ns) %>% dplyr::mutate(study='Study 3')

p.eff.mv.rt.ns<-ggplot(data=IA.mv.RT.ns, aes(x=scaledMeanValue, y=fit, group=catChoiceCondition)) +
  geom_line(size=0.5,aes(linetype=study,color=catChoiceCondition))+theme_bw(12) +
  geom_ribbon(data=IA.mv.RT.ns, aes(x=scaledMeanValue, max = upper, min = lower,fill=catChoiceCondition),alpha=0.3, inherit.aes = FALSE)+ 
  xlab("Overall Value\n(z-scored)") + ylab("RT (Log-Transformed)") + 
  theme(panel.border = element_blank(), panel.grid.major = element_blank(),
        axis.title.x = element_text(margin = margin(t = 0, r = 0, b = 0, l = 0)),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),
        axis.ticks = element_line(colour = "black",size=0.2)) +
  theme(legend.justification=c(1,1),legend.position='none',text = element_text(size=6)) + 
  scale_fill_manual("",values=c('#0673C3','#00B024')) + 
  scale_color_manual("",values=c('#0673C3','#00B024')) + 
  coord_cartesian(ylim=c(.3,.7)) + scale_y_continuous(breaks = c(.3,.7))

p.eff.mv.rt.ns

eff_vd.RT.ns <- Effect(c("scaledValueDiff","catChoiceCondition"),
                   model.RT.ns,
                   xlevels=list(scaledValueDiff=seq(quantile(df.total.rt.new.s$scaledValueDiff,0.025),
                                                    quantile(df.total.rt.new.s$scaledValueDiff,0.975),0.1)))

## Warning in Analyze.model(focal.predictors, mod, xlevels, default.levels, : the
## predictors scaledMeanValue, scaledValueDiff, scaledTrialNum are one-column
## matrices that were converted to vectors

IA.vd.RT.ns <- as.data.frame(eff_vd.RT.ns) %>% dplyr::mutate(study='Study 3')

p.eff.vd.rt.ns<-ggplot(data=IA.vd.RT.ns, aes(x=scaledValueDiff, y=fit, group=catChoiceCondition)) +
  geom_line(size=0.5,aes(linetype=study,color=catChoiceCondition))+theme_bw(12) +
  geom_ribbon(data=IA.vd.RT.ns, aes(x=scaledValueDiff, max = upper, min = lower,fill=catChoiceCondition),alpha=0.3, inherit.aes = FALSE)+ 
  xlab("Relative Value\n(z-scored)") + ylab("RT (Log-Transformed)") + 
  theme(panel.border = element_blank(), panel.grid.major = element_blank(),
        axis.title.x = element_text(margin = margin(t = 0, r = 0, b = 0, l = 0)),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),
        axis.ticks = element_line(colour = "black",size=0.2)) +
  theme(legend.justification=c(1,1),legend.position='none',text = element_text(size=6)) + 
  scale_fill_manual("",values=c('#0673C3','#00B024')) + 
  scale_color_manual("",values=c('#0673C3','#00B024')) + 
  coord_cartesian(ylim=c(.3,.7)) + scale_y_continuous(breaks = c(.3,.7))

p.eff.vd.rt.ns

eff_mv.acc.ns <- Effect(c("scaledMeanValue","catChoiceCondition"),
                   model.acc.ns,
                   xlevels=list(scaledMeanValue=seq(quantile(df.total.rt.new.s$scaledMeanValue,0.025),
                                                    quantile(df.total.rt.new.s$scaledMeanValue,0.972),0.1)))

## Warning in Analyze.model(focal.predictors, mod, xlevels, default.levels, : the
## predictors scaledMeanValue, scaledValueDiff, scaledTrialNum are one-column
## matrices that were converted to vectors

IA.mv.acc.ns <- as.data.frame(eff_mv.acc.ns) %>% dplyr::mutate(study='Study 3')

p.eff.mv.acc.ns <-ggplot(data=IA.mv.acc.ns, aes(x=scaledMeanValue, y=fit, group=catChoiceCondition)) +
  geom_line(size=0.5,aes(linetype=study,color=catChoiceCondition))+theme_bw(12) +
  geom_ribbon(data=IA.mv.acc.ns, aes(x=scaledMeanValue, max = upper, min = lower,fill=catChoiceCondition),alpha=0.3, inherit.aes = FALSE)+ 
  xlab("Overall value\n(z-scored)") + ylab("P(Best First)") + 
  theme(panel.border = element_blank(), panel.grid.major = element_blank(), 
        axis.title.x = element_text(margin = margin(t = 0, r = 0, b = 0, l = 0)),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),
        axis.ticks = element_line(colour = "black",size=0.2)) +
  theme(legend.justification=c(1,1),legend.position='none',text = element_text(size=6)) + 
  scale_fill_manual("",values=c('#0673C3','#00B024')) + 
  scale_color_manual("",values=c('#0673C3','#00B024')) + 
  coord_cartesian(ylim=c(0.1,0.9)) + scale_y_continuous(breaks = c(0.1,0.9),labels=function(x) sprintf("%.1f", x))

p.eff.mv.acc.ns

#ggsave('Study12_RT.pdf')

eff_vd.acc.ns <- Effect(c("scaledValueDiff","catChoiceCondition"),
                   model.acc.ns,
                   xlevels=list(scaledValueDiff=seq(quantile(df.total.rt.new.s$scaledValueDiff,0.025),
                                                    quantile(df.total.rt.new.s$scaledValueDiff,0.975),0.1)))

## Warning in Analyze.model(focal.predictors, mod, xlevels, default.levels, : the
## predictors scaledMeanValue, scaledValueDiff, scaledTrialNum are one-column
## matrices that were converted to vectors

IA.vd.acc.ns <- as.data.frame(eff_vd.acc.ns) %>% dplyr::mutate(study='Study 3')

p.eff.vd.acc.ns<-ggplot(data=IA.vd.acc.ns, aes(x=scaledValueDiff, y=fit, group=catChoiceCondition)) +
  geom_line(size=0.5,aes(linetype=study,color=catChoiceCondition))+theme_bw(12) +
  geom_ribbon(data=IA.vd.acc.ns, aes(x=scaledValueDiff, max = upper, min = lower,fill=catChoiceCondition),alpha=0.3, inherit.aes = FALSE)+ 
  xlab("Relative Value\n(z-scored)") + ylab("P(Best First)") + 
  theme(panel.border = element_blank(), panel.grid.major = element_blank(), 
        axis.title.x = element_text(margin = margin(t = 0, r = 0, b = 0, l = 0)),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),
        axis.ticks = element_line(colour = "black",size=0.2)) +
  theme(legend.justification=c(1,1),legend.position='none',text = element_text(size=6)) + 
  scale_fill_manual("",values=c('#0673C3','#00B024')) + 
  scale_color_manual("",values=c('#0673C3','#00B024')) + 
  coord_cartesian(ylim=c(0.1,0.9)) + scale_y_continuous(breaks = c(0.1,0.9),labels=function(x) sprintf("%.1f", x))

p.eff.vd.acc.ns

#ggsave('Study12_RT.pdf')

lay <- rbind(c(1,NA,2,NA,3),
             c(4,NA,5,NA,6))

plots <- list(p.diff.rt.ns,p.eff.mv.rt.ns,p.eff.vd.rt.ns,
              p.diff.acc.ns,p.eff.mv.acc.ns,p.eff.vd.acc.ns)
grobs <- list()
widths <- list()
heights <- list()

for (i in 1:length(plots)){
    grobs[[i]] <- ggplotGrob(plots[[i]])
    widths[[i]] <- grobs[[i]]$widths
    heights[[i]] <- grobs[[i]]$heights
}

maxwidth <- do.call(grid::unit.pmax, widths)
maxheight <- do.call(grid::unit.pmax,heights)

for (i in 1:length(grobs)){
     grobs[[i]]$heights <- as.list(maxheight)
     grobs[[i]]$widths <- as.list(maxwidth)
}


for (i in 1:length(grobs)){
     grobs[[i]]$heights <- as.list(maxheight)
     grobs[[i]]$widths <- as.list(maxwidth)
}


p<-grid.arrange(grobs = grobs, layout_matrix = lay,widths=unit(c(2,0.1,2.7,0.1,2.7), c("cm", "cm")),heights=unit(c(3,3),c('cm','cm')))

ggsave(filename = '../Figures/FigureS1.pdf',p,units = 'cm',width = 20,height = 12)

coeff.rt <- t(fixef(model.RT.nd)['catChoiceConditionOR-XOR'])
df.ci <- confint(model.RT.nd,method="Wald")
df.ci <- df.ci[!is.na(df.ci[,1]),]
ci.rt <- df.ci['catChoiceConditionOR-XOR',]
estimate.rt <- cbind(coeff.rt,t(ci.rt))
colnames(estimate.rt)<-c('coeff','lower','upper')

coeff.acc <- t(fixef(model.acc.nd.dummy)['catChoiceConditionOR-XOR'])
df.ci <- confint(model.acc.nd.dummy,method="Wald")
df.ci <- df.ci[!is.na(df.ci[,1]),]
ci.acc <- df.ci['catChoiceConditionOR-XOR',]
estimate.acc <- cbind(coeff.acc,t(ci.acc))
colnames(estimate.acc)<-c('coeff','lower','upper')

coeff.conf <- t(fixef(model.rating.nd)['catChoiceConditionOR-XOR'])
df.ci <- confint(model.rating.nd,method="Wald")
df.ci <- df.ci[!is.na(df.ci[,1]),]
ci.conf <- df.ci['catChoiceConditionOR-XOR',]
estimate.conf <- cbind(coeff.conf,t(ci.conf))
colnames(estimate.conf)<-c('coeff','lower','upper')

estimate.all <- data.frame(rbind(estimate.rt,estimate.acc,estimate.conf))
estimate.all$var <- c('RT','Acc','Conflict')

p.diff.acc.nd <- ggplot(estimate.all %>% filter(var %in% c('Acc')), aes(x=var, y=coeff))  + geom_hline(yintercept=0,color='#555555',size=0.2) + 
  geom_point(stat="identity", position=position_dodge(0.6),size=0.5) +
  geom_errorbar(aes(ymin=lower, ymax=upper), width=0.1,size=0.4,
                 position=position_dodge(.6))+labs(x="", y = "Effect of Inclusivity")+theme_bw(12) + 
  theme(panel.border = element_blank(),panel.grid.major = element_blank(),
        axis.title.x = element_text(margin = margin(t = 0, r = 0, b = 0, l = 0)),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),
        axis.ticks = element_line(colour = "black",size=0.2),
        text=element_text(size=6),legend.position="none") +
  scale_x_discrete(labels=c("Acc"='P(Worst First)')) + scale_y_continuous(limits = c(-0.05,0.05),breaks = c(-0.05,0.05))

p.diff.acc.nd

p.diff.rt.nd <- ggplot(estimate.all %>% filter(var %in% c('RT')), aes(x=var, y=coeff))  + geom_hline(yintercept=0,color='#555555',size=0.2) + 
  geom_point(stat="identity", position=position_dodge(0.6),size=0.5) +
  geom_errorbar(aes(ymin=lower, ymax=upper), width=0.1,size=0.4,
                 position=position_dodge(.6))+labs(x="", y = "Effect of Inclusivity")+theme_bw(12) + 
  theme(panel.border = element_blank(),panel.grid.major = element_blank(),
        axis.title.x = element_text(margin = margin(t = 0, r = 0, b = 0, l = 0)),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),
        axis.ticks = element_line(colour = "black",size=0.2),
        text=element_text(size=6),legend.position="none") +
  scale_x_discrete(labels=c("RT"='log(RT)')) + 
  scale_color_manual(values=c('#0673C3','#00B024')) + scale_y_continuous(limits = c(-0.05,0.005),breaks = c(-0.05,0))

p.diff.rt.nd

p.diff.conflict.nd <- ggplot(estimate.all %>% filter(var %in% c('Conflict')), aes(x=var, y=coeff))  + geom_hline(yintercept=0,color='#555555',size=0.2) + 
  geom_point(stat="identity", position=position_dodge(0.6),size=0.5) +
  geom_errorbar(aes(ymin=lower, ymax=upper), width=0.1,size=0.4,
                 position=position_dodge(.6))+labs(x="", y = "Effect of Inclusivity")+theme_bw(12) + 
  theme(panel.border = element_blank(),panel.grid.major = element_blank(),
        axis.title.x = element_text(margin = margin(t = 0, r = 0, b = 0, l = 0)),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),
        axis.ticks = element_line(colour = "black",size=0.2),
        text=element_text(size=6),legend.position="none") +
  scale_x_discrete(labels=c("Conflict"='Conflict')) + 
  scale_color_manual(values=c('#0673C3','#00B024')) + scale_y_continuous(limits = c(-0.5,0.1),breaks = c(-0.5,0))
p.diff.conflict.nd

eff_mv.RT.nd <- Effect(c("scaledMeanValue","catChoiceCondition"),
                   model.RT.nd,
                   xlevels=list(scaledMeanValue=seq(quantile(df.total.rt.new.s$scaledMeanValue,0.025),
                                                    quantile(df.total.rt.new.s$scaledMeanValue,0.975),0.1)))

## Warning in Analyze.model(focal.predictors, mod, xlevels, default.levels, : the
## predictors scaledMeanValue, scaledValueDiff, scaledTrialNum are one-column
## matrices that were converted to vectors

IA.mv.RT.nd <- as.data.frame(eff_mv.RT.nd) %>% dplyr::mutate(study='Study 3')

p.eff.mv.rt.nd<-ggplot(data=IA.mv.RT.nd, aes(x=scaledMeanValue, y=fit, group=catChoiceCondition)) +
  geom_line(size=0.5,aes(linetype=study,color=catChoiceCondition))+theme_bw(12) +
  geom_ribbon(data=IA.mv.RT.nd, aes(x=scaledMeanValue, max = upper, min = lower,fill=catChoiceCondition),alpha=0.3, inherit.aes = FALSE)+ 
  xlab("Overall Value\n(z-scored)") + ylab("RT (Log-Transformed)") + 
  theme(panel.border = element_blank(), panel.grid.major = element_blank(),
        axis.title.x = element_text(margin = margin(t = 0, r = 0, b = 0, l = 0)),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),
        axis.ticks = element_line(colour = "black",size=0.2)) +
  theme(legend.justification=c(1,1),legend.position='none',text = element_text(size=6)) + 
  scale_fill_manual("",values=c('#0673C3','#00B024')) + 
  scale_color_manual("",values=c('#0673C3','#00B024')) + 
  coord_cartesian(ylim=c(.2,.7)) + scale_y_continuous(breaks = c(.2,.7))

p.eff.mv.rt.nd

eff_vd.RT.nd <- Effect(c("scaledValueDiff","catChoiceCondition"),
                   model.RT.nd,
                   xlevels=list(scaledValueDiff=seq(quantile(df.total.rt.new.s$scaledValueDiff,0.025),
                                                    quantile(df.total.rt.new.s$scaledValueDiff,0.975),0.1)))

## Warning in Analyze.model(focal.predictors, mod, xlevels, default.levels, : the
## predictors scaledMeanValue, scaledValueDiff, scaledTrialNum are one-column
## matrices that were converted to vectors

IA.vd.RT.nd <- as.data.frame(eff_vd.RT.nd) %>% dplyr::mutate(study='Study 3')

p.eff.vd.rt.nd<-ggplot(data=IA.vd.RT.nd, aes(x=scaledValueDiff, y=fit, group=catChoiceCondition)) +
  geom_line(size=0.5,aes(linetype=study,color=catChoiceCondition))+theme_bw(12) +
  geom_ribbon(data=IA.vd.RT.nd, aes(x=scaledValueDiff, max = upper, min = lower,fill=catChoiceCondition),alpha=0.3, inherit.aes = FALSE)+ 
  xlab("Relative Value\n(z-scored)") + ylab("RT (Log-Transformed)") + 
  theme(panel.border = element_blank(), panel.grid.major = element_blank(),
        axis.title.x = element_text(margin = margin(t = 0, r = 0, b = 0, l = 0)),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),axis.ticks = element_line(colour = "black",size=0.2)) +
  theme(legend.justification=c(1,1),legend.position='none',text = element_text(size=6)) + 
  scale_fill_manual("",values=c('#0673C3','#00B024')) + 
  scale_color_manual("",values=c('#0673C3','#00B024')) + 
  coord_cartesian(ylim=c(.2,.7)) + scale_y_continuous(breaks = c(.2,.7))

p.eff.vd.rt.nd

eff_mv.acc.nd <- Effect(c("scaledMeanValue","catChoiceCondition"),
                   model.acc.nd,
                   xlevels=list(scaledMeanValue=seq(quantile(df.total.rt.new.s$scaledMeanValue,0.025),
                                                    quantile(df.total.rt.new.s$scaledMeanValue,0.972),0.1)))

## Warning in Analyze.model(focal.predictors, mod, xlevels, default.levels, : the
## predictors scaledMeanValue, scaledValueDiff, scaledTrialNum are one-column
## matrices that were converted to vectors

IA.mv.acc.nd <- as.data.frame(eff_mv.acc.nd) %>% dplyr::mutate(study='Study 3')

p.eff.mv.acc.nd <-ggplot(data=IA.mv.acc.nd, aes(x=scaledMeanValue, y=fit, group=catChoiceCondition)) +
  geom_line(size=0.5,aes(linetype=study,color=catChoiceCondition))+theme_bw(12) +
  geom_ribbon(data=IA.mv.acc.nd, aes(x=scaledMeanValue, max = upper, min = lower,fill=catChoiceCondition),alpha=0.3, inherit.aes = FALSE)+ 
  xlab("Overall value\n(z-scored)") + ylab("P(Worst First)") + 
  theme(panel.border = element_blank(), panel.grid.major = element_blank(),
        axis.title.x = element_text(margin = margin(t = 0, r = 0, b = 0, l = 0)),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),axis.ticks = element_line(colour = "black",size=0.2)) +
  theme(legend.justification=c(1,1),legend.position='none',text = element_text(size=6)) + 
  scale_fill_manual("",values=c('#0673C3','#00B024')) + 
  scale_color_manual("",values=c('#0673C3','#00B024')) + 
  coord_cartesian(ylim=c(0.1,0.9)) + scale_y_continuous(breaks = c(0.1,0.9),labels=function(x) sprintf("%.1f", x))

p.eff.mv.acc.nd

#ggsave('Study12_RT.pdf')

eff_vd.acc.nd <- Effect(c("scaledValueDiff","catChoiceCondition"),
                   model.acc.nd,
                   xlevels=list(scaledValueDiff=seq(quantile(df.total.rt.new.s$scaledValueDiff,0.025),
                                                    quantile(df.total.rt.new.s$scaledValueDiff,0.975),0.1)))

## Warning in Analyze.model(focal.predictors, mod, xlevels, default.levels, : the
## predictors scaledMeanValue, scaledValueDiff, scaledTrialNum are one-column
## matrices that were converted to vectors

IA.vd.acc.nd <- as.data.frame(eff_vd.acc.nd) %>% dplyr::mutate(study='Study 3')

p.eff.vd.acc.nd<-ggplot(data=IA.vd.acc.nd, aes(x=scaledValueDiff, y=fit, group=catChoiceCondition)) +
  geom_line(size=0.5,aes(linetype=study,color=catChoiceCondition))+theme_bw(12) +
  geom_ribbon(data=IA.vd.acc.nd, aes(x=scaledValueDiff, max = upper, min = lower,fill=catChoiceCondition),alpha=0.3, inherit.aes = FALSE)+ 
  xlab("Relative Value\n(z-scored)") + ylab("P(Worst First)") + 
  theme(panel.border = element_blank(), panel.grid.major = element_blank(),
        axis.title.x = element_text(margin = margin(t = 0, r = 0, b = 0, l = 0)),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),axis.ticks = element_line(colour = "black",size=0.2)) +
  theme(legend.justification=c(1,1),legend.position='none',text = element_text(size=6)) + 
  scale_fill_manual("",values=c('#0673C3','#00B024')) + 
  scale_color_manual("",values=c('#0673C3','#00B024')) + 
  coord_cartesian(ylim=c(0.1,0.9)) + scale_y_continuous(breaks = c(0.1,0.9),labels=function(x) sprintf("%.1f", x))

p.eff.vd.acc.nd

#ggsave('Study12_RT.pdf')

lay <- rbind(c(1,NA,2,NA,3),
             c(4,NA,5,NA,6))

plots <- list(p.diff.rt.nd,p.eff.mv.rt.nd,p.eff.vd.rt.nd,
              p.diff.acc.nd,p.eff.mv.acc.nd,p.eff.vd.acc.nd)
grobs <- list()
widths <- list()
heights <- list()

for (i in 1:length(plots)){
    grobs[[i]] <- ggplotGrob(plots[[i]])
    widths[[i]] <- grobs[[i]]$widths
    heights[[i]] <- grobs[[i]]$heights
}

maxwidth <- do.call(grid::unit.pmax, widths)
maxheight <- do.call(grid::unit.pmax,heights)

for (i in 1:length(grobs)){
     grobs[[i]]$heights <- as.list(maxheight)
     grobs[[i]]$widths <- as.list(maxwidth)
}


for (i in 1:length(grobs)){
     grobs[[i]]$heights <- as.list(maxheight)
     grobs[[i]]$widths <- as.list(maxwidth)
}


p<-grid.arrange(grobs = grobs, layout_matrix = lay,widths=unit(c(2,0.1,2.7,0.1,2.7), c("cm", "cm")),heights=unit(c(3,3),c('cm','cm')))

ggsave(filename = '../Figures/FigureS2.pdf',p,units = 'cm',width = 20,height = 12)

eff_mv.cfl.ns <- Effect(c("scaledMeanValue","catChoiceCondition"),
                       model.rating.ns,
                       xlevels=list(scaledMeanValue=seq(quantile(df.total.new.s$scaledMeanValue,0.025),
                                                        quantile(df.total.new.s$scaledMeanValue,0.975),0.1)))

## Warning in Analyze.model(focal.predictors, mod, xlevels, default.levels, : the
## predictors scaledValueDiff, scaledTrialNum, scaledMeanValue are one-column
## matrices that were converted to vectors

IA.mv.cfl.ns <- as.data.frame(eff_mv.cfl.ns) %>% dplyr::mutate(study='Study 3')

IA.mv.cfl <- IA.mv.cfl.ns

IA.mv.cfl$catChoiceCondition <- relevel(IA.mv.cfl$catChoiceCondition,ref = 'XOR')

p.eff.mv.cfl.ns<-ggplot(data=IA.mv.cfl, aes(x=scaledMeanValue, y=fit,group=catChoiceCondition)) +
  geom_line(size=0.5,aes(linetype=study,color=catChoiceCondition))+theme_bw(12) +
  geom_ribbon(data=IA.mv.cfl, aes(x=scaledMeanValue, max = upper, min = lower,fill=catChoiceCondition),alpha=0.3, inherit.aes = FALSE)+ 
  xlab("Overall value\n(z-scored)") + ylab("Conflict") + 
  theme(panel.border = element_blank(), panel.grid.major = element_blank(),
        axis.title.x = element_text(margin = margin(t = 0, r = 0, b = 0, l = 0)),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),axis.ticks = element_line(colour = "black",size=0.2)) +
  theme(legend.justification=c(1,1),legend.position='none',text = element_text(size=6)) + 
  scale_fill_manual("",values=c('#0673C3','#00B024')) + 
  scale_color_manual("",values=c('#0673C3','#00B024')) + # ggtitle('Exclusive') +
  coord_cartesian(ylim=c(1,4)) + scale_y_continuous(breaks = c(1,4))

p.eff.mv.cfl.ns

# ggsave('figures/ov_conflict_by_cond_d.pdf',width=4,height=2.5)

new.mv.1 <- seq(quantile(df.total.new.s$scaledMeanValue,0.025),
                quantile(df.total.new.s$scaledMeanValue,0.975),0.1)

eff.df.mv.ns <- marginalConflictMVEffect(model.rating.ns,df.total.rt.new.s$scaledMeanValue,new.mv.1) %>%
  dplyr::mutate(scaledMeanValue=x,
                catChoiceCondition='XOR - OR',
                fit= eff,
                upper= eff+ci,
                lower= eff-ci,
                se=NA,
                study='Study 3')

p.eff.cc.int.ns<-ggplot(data=eff.df.mv.ns, aes(x=x, y=fit)) + 
  geom_line(size=0.5)+theme_bw(12) +
  geom_ribbon(data=eff.df.mv.ns, aes(x=x, max = upper, min = lower),alpha=0.3, inherit.aes = FALSE)+ 
  xlab("Overall value\n(z-scored)") + ylab('Effect of Inclusivity') +
  theme(panel.border = element_blank(), panel.grid.major = element_blank(),
        axis.title.x = element_text(margin = margin(t = 0, r = 0, b = 0, l = 0)),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),axis.ticks = element_line(colour = "black",size=0.2)) +
  theme(legend.justification=c(1,1),legend.position='none',text = element_text(size=6)) + geom_hline(yintercept=0,color='#555555',size=0.2) + 
  scale_fill_manual("",values=c("#005555","#550055")) + scale_color_manual("",values=c("#005555","#550055")) + # ggtitle('Exclusive - Non-Exclusive') +
  coord_cartesian(ylim=c(-1,0.2)) + scale_y_continuous(breaks = c(-1,0))

p.eff.cc.int.ns

eff_vd.cfl.ns <- Effect(c("scaledValueDiff","catChoiceCondition"),
                   model.rating.ns,
                   xlevels=list(scaledValueDiff=seq(quantile(df.total.new.s$scaledValueDiff,0.025),
                                                    quantile(df.total.new.s$scaledValueDiff,0.975),0.1)))

## Warning in Analyze.model(focal.predictors, mod, xlevels, default.levels, : the
## predictors scaledValueDiff, scaledTrialNum, scaledMeanValue are one-column
## matrices that were converted to vectors

IA.vd.cfl <- as.data.frame(eff_vd.cfl.ns) %>% dplyr::mutate(study='Study 1')

IA.vd.cfl$catChoiceCondition <- relevel(IA.vd.cfl$catChoiceCondition,ref = 'XOR')

p.eff.vd.cfl.ns<-ggplot(data=IA.vd.cfl, aes(x=scaledValueDiff, y=fit,group=catChoiceCondition)) +
  geom_line(size=0.5,aes(color=catChoiceCondition))+theme_bw(12) +
  geom_ribbon(data=IA.vd.cfl, aes(x=scaledValueDiff, max = upper, min = lower,fill=catChoiceCondition),alpha=0.3, inherit.aes = FALSE)+ 
  xlab("Relative Value\n(z-scored)") + ylab("Conflict") + 
  theme(panel.border = element_blank(), panel.grid.major = element_blank(),
        axis.title.x = element_text(margin = margin(t = 0, r = 0, b = 0, l = 0)),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),axis.ticks = element_line(colour = "black",size=0.2)) +
  theme(legend.justification=c(1,1),legend.position='none',text = element_text(size=6)) + 
  scale_fill_manual("",values=c('#0673C3','#00B024','#008012')) + 
  scale_color_manual("",values=c('#0673C3','#00B024','#008012')) + 
  coord_cartesian(ylim=c(1,4)) + scale_y_continuous(breaks = c(1,4))

p.eff.vd.cfl.ns

#ggsave('Study12_RT.pdf')

lay <- rbind(c(1,NA,2,NA,3,NA,4))

plots <- list(p.diff.conflict.ns,p.eff.mv.cfl.ns,p.eff.cc.int.ns,p.eff.vd.cfl.ns)
grobs <- list()
widths <- list()
heights <- list()

for (i in 1:length(plots)){
    grobs[[i]] <- ggplotGrob(plots[[i]])
    widths[[i]] <- grobs[[i]]$widths
    heights[[i]] <- grobs[[i]]$heights
}

maxwidth <- do.call(grid::unit.pmax, widths)
maxheight <- do.call(grid::unit.pmax, heights)

for (i in 1:length(grobs)){
  grobs[[i]]$widths <- as.list(maxwidth)
  grobs[[i]]$heights <- as.list(maxheight)
}

p<-grid.arrange(grobs = grobs, layout_matrix = lay,widths=unit(c(1.8,0.1,2.7,0.1,2.7,0.1,2.7), c("cm", "cm")),heights=unit(c(3),c('cm','cm')))

ggsave(filename = '../Figures/FigureS3.pdf',p,units = 'cm',width = 25,height = 12)

eff_mv.cfl.nd <- Effect(c("scaledMeanValue","catChoiceCondition"),
                       model.rating.nd,
                       xlevels=list(scaledMeanValue=seq(quantile(df.total.new.d$scaledMeanValue,0.025),
                                                        quantile(df.total.new.d$scaledMeanValue,0.975),0.1)))

## Warning in Analyze.model(focal.predictors, mod, xlevels, default.levels, : the
## predictors scaledValueDiff, scaledTrialNum, scaledMeanValue are one-column
## matrices that were converted to vectors

IA.mv.cfl.nd <- as.data.frame(eff_mv.cfl.nd) %>% dplyr::mutate(study='Study 3')

IA.mv.cfl <- IA.mv.cfl.nd

IA.mv.cfl$catChoiceCondition <- relevel(IA.mv.cfl$catChoiceCondition,ref = 'XOR')

p.eff.mv.cfl.nd<-ggplot(data=IA.mv.cfl, aes(x=scaledMeanValue, y=fit,group=catChoiceCondition)) +
  geom_line(size=0.5,aes(linetype=study,color=catChoiceCondition))+theme_bw(12) +
  geom_ribbon(data=IA.mv.cfl, aes(x=scaledMeanValue, max = upper, min = lower,fill=catChoiceCondition),alpha=0.3, inherit.aes = FALSE)+ 
  xlab("Overall value\n(z-scored)") + ylab("Conflict") + 
  theme(panel.border = element_blank(), panel.grid.major = element_blank(),
        axis.title.x = element_text(margin = margin(t = 0, r = 0, b = 0, l = 0)),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),axis.ticks = element_line(colour = "black",size=0.2)) +
  theme(legend.justification=c(1,1),legend.position='none',text = element_text(size=6)) + 
  scale_fill_manual("",values=c('#0673C3','#00B024')) + 
  scale_color_manual("",values=c('#0673C3','#00B024')) + # ggtitle('Exclusive') +
  coord_cartesian(ylim=c(1,4)) + scale_y_continuous(breaks = c(1,4))

p.eff.mv.cfl.nd

# ggsave('figures/ov_conflict_by_cond_d.pdf',width=4,height=2.5)

new.mv.1 <- seq(quantile(df.total.new.d$scaledMeanValue,0.025),
                quantile(df.total.new.d$scaledMeanValue,0.975),0.1)

eff.df.mv.nd <- marginalConflictMVEffect(model.rating.nd,df.total.new.d$scaledMeanValue,new.mv.1) %>%
  dplyr::mutate(scaledMeanValue=x,
                catChoiceCondition='XOR - OR',
                fit= eff,
                upper= eff+ci,
                lower= eff-ci,
                se=NA,
                study='Study 3')

p.eff.cc.int.nd<-ggplot(data=eff.df.mv.nd, aes(x=x, y=fit)) + 
  geom_line(size=0.5)+theme_bw(12) +
  geom_ribbon(data=eff.df.mv.nd, aes(x=x, max = upper, min = lower),alpha=0.3, inherit.aes = FALSE)+ 
  xlab("Overall value\n(z-scored)") + ylab('Effect of Inclusivity') +
  theme(panel.border = element_blank(), panel.grid.major = element_blank(),
        axis.title.x = element_text(margin = margin(t = 0, r = 0, b = 0, l = 0)),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),axis.ticks = element_line(colour = "black",size=0.2)) +
  theme(legend.justification=c(1,1),legend.position='none',text = element_text(size=6)) + geom_hline(yintercept=0,color='#555555',size=0.2) + 
  scale_fill_manual("",values=c("#005555","#550055")) + scale_color_manual("",values=c("#005555","#550055")) + # ggtitle('Exclusive - Non-Exclusive') +
  coord_cartesian(ylim=c(-1,0.2)) + scale_y_continuous(breaks = c(-1,0))

p.eff.cc.int.nd

eff_vd.cfl.nd <- Effect(c("scaledValueDiff","catChoiceCondition"),
                   model.rating.nd,
                   xlevels=list(scaledValueDiff=seq(quantile(df.total.new.d$scaledValueDiff,0.025),
                                                    quantile(df.total.new.d$scaledValueDiff,0.975),0.1)))

## Warning in Analyze.model(focal.predictors, mod, xlevels, default.levels, : the
## predictors scaledValueDiff, scaledTrialNum, scaledMeanValue are one-column
## matrices that were converted to vectors

IA.vd.cfl <- as.data.frame(eff_vd.cfl.nd) %>% dplyr::mutate(study='Study 1')

IA.vd.cfl$catChoiceCondition <- relevel(IA.vd.cfl$catChoiceCondition,ref = 'XOR')

p.eff.vd.cfl.nd<-ggplot(data=IA.vd.cfl, aes(x=scaledValueDiff, y=fit,group=catChoiceCondition)) +
  geom_line(size=0.5,aes(color=catChoiceCondition))+theme_bw(12) +
  geom_ribbon(data=IA.vd.cfl, aes(x=scaledValueDiff, max = upper, min = lower,fill=catChoiceCondition),alpha=0.3, inherit.aes = FALSE)+ 
  xlab("Relative Value\n(z-scored)") + ylab("Conflict") + theme(panel.border = element_blank(), panel.grid.major = element_blank(),
        axis.title.x = element_text(margin = margin(t = 0, r = 0, b = 0, l = 0)),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),axis.ticks = element_line(colour = "black",size=0.2)) +
  theme(legend.justification=c(1,1),legend.position='none',text = element_text(size=6)) + 
  scale_fill_manual("",values=c('#0673C3','#00B024','#008012')) + 
  scale_color_manual("",values=c('#0673C3','#00B024','#008012')) + 
  coord_cartesian(ylim=c(1,4)) + scale_y_continuous(breaks = c(1,4))

p.eff.vd.cfl.nd

#ggsave('Study12_RT.pdf')

lay <- rbind(c(1,NA,2,NA,3,NA,4))

plots <- list(p.diff.conflict.nd,p.eff.mv.cfl.nd,p.eff.cc.int.nd,p.eff.vd.cfl.nd)
grobs <- list()
widths <- list()
heights <- list()

for (i in 1:length(plots)){
    grobs[[i]] <- ggplotGrob(plots[[i]])
    widths[[i]] <- grobs[[i]]$widths
    heights[[i]] <- grobs[[i]]$heights
}

maxwidth <- do.call(grid::unit.pmax, widths)
maxheight <- do.call(grid::unit.pmax, heights)

for (i in 1:length(grobs)){
  grobs[[i]]$widths <- as.list(maxwidth)
  grobs[[i]]$heights <- as.list(maxheight)
}

p<-grid.arrange(grobs = grobs, layout_matrix = lay,widths=unit(c(1.8,0.1,2.7,0.1,2.7,0.1,2.7), c("cm", "cm")),heights=unit(c(3),c('cm','cm')))

ggsave(filename = '../Figures/FigureS4.pdf',p,units = 'cm',width = 25,height = 12)

5 All about the voluntary choices

df.or.rt.12 <- df.total.rt.12 %>% filter(catChoiceCondition=='OR') %>%
    dplyr::mutate(scaledMeanValue=scale(meanValue),
                  scaledValueDiff=scale(valueDiff),
                  scaledTrialNum=scale(trialN),
                  scaledFirstRT=scale(firstRT))


df.or.rt.3 <- df.total.rt.3 %>% filter(catChoiceCondition=='OR') %>%
    dplyr::mutate(scaledMeanValue=scale(meanValue),
                  scaledValueDiff=scale(valueDiff),
                  scaledTrialNum=scale(trialN),
                  scaledFirstRT=scale(firstRT))

df.or.rt.12.kept <- inner_join(df.or.rt.12,
                               rbind(df.rating.1.summary,df.rating.2.summary),by='participant') %>% 
  rowwise() %>%
  dplyr::mutate(valueKept = getMeanChosen(c(Value1,Value2,Value3,Value4),
                                          c(Order1,Order2,Order3,Order4)),
                minKept=getMinChosen(c(Value1,Value2,Value3,Value4),
                                     c(Order1,Order2,Order3,Order4)),
                NUFKept=getNUFChosen(c(Value1,Value2,Value3,Value4),
                                     c(Order1,Order2,Order3,Order4),
                                     medianValue),
                NUFKept2=getNUFChosen(c(Value1,Value2,Value3,Value4),
                                     c(Order1,Order2,Order3,Order4),
                                     avgValue),
                NUF=getNUF(c(Value1,Value2,Value3,Value4),medianValue),
                NUF2=getNUF(c(Value1,Value2,Value3,Value4),avgValue)) %>% ungroup()

# df.or.rt.12.kept <- inner_join(df.or.rt.12.kept,rbind(df.rating.1.summary,df.rating.2.summary),by='participant')

df.or.rt.new.s.kept <- inner_join(df.or.rt.new.s,df.rating.new.s,by='participant') %>% rowwise() %>%
  dplyr::mutate(valueKept = getMeanChosen(c(Value1,Value2,Value3,Value4),
                                          c(Order1,Order2,Order3,Order4)),
                minKept=getMinChosen(c(Value1,Value2,Value3,Value4),
                                     c(Order1,Order2,Order3,Order4)),
                NUFKept=getNUFChosen(c(Value1,Value2,Value3,Value4),
                                     c(Order1,Order2,Order3,Order4),
                                     medianValue),
                NUFKept2=getNUFChosen(c(Value1,Value2,Value3,Value4),
                                     c(Order1,Order2,Order3,Order4),
                                     avgValue),
                NUF=getNUF(c(Value1,Value2,Value3,Value4),medianValue),
                NUF2=getNUF(c(Value1,Value2,Value3,Value4),avgValue)) %>% ungroup()

# df.or.rt.new.s.kept <- inner_join(df.or.rt.new.s.kept,df.rating.new.s,by='participant')

df.s.combined.or <- rbind(df.or.rt.12.kept %>% select(minKept,valueKept,NUFKept,NChosen,NUF,NUFKept2,NUF2,conflict,meanValue,medianValue,valueDiff,trialN,firstRT,acc,participant) %>% mutate(study='old'),
                          df.or.rt.new.s.kept %>% filter(firstRT<15) %>% select(minKept,valueKept,NUFKept,NChosen,NUF,NUFKept2,NUF2,conflict,meanValue,medianValue,valueDiff,trialN,firstRT,acc,participant) %>% mutate(study='new')) %>% ungroup() %>%
  dplyr::mutate(scaledMeanValue=scale(meanValue),
         scaledValueDiff=scale(valueDiff),
         scaledTrialNum=scale(trialN),
         scaledFirstRT=scale(firstRT),
         scaledConflict=scale(conflict),
         scaledNUF=scale(NUF),
         scaledNUF2=scale(NUF2),
         study=factor(study))

contrasts(df.s.combined.or$acc)<-contr.sum
contrasts(df.s.combined.or$study)<-contr.sum

df.or.rt.3.kept <- inner_join(df.or.rt.3,
                               df.rating.3.summary,by='participant') %>% 
  rowwise() %>%
  dplyr::mutate(valueKept = getMeanUnChosen(c(Value1,Value2,Value3,Value4),
                                          c(Order1,Order2,Order3,Order4)),
                minKept=getMinUnChosen(c(Value1,Value2,Value3,Value4),
                                     c(Order1,Order2,Order3,Order4)),
                NUFKept=getNUFUnChosen(c(Value1,Value2,Value3,Value4),
                                     c(Order1,Order2,Order3,Order4),
                                     medianValue),
                NUFKept2=getNUFUnChosen(c(Value1,Value2,Value3,Value4),
                                     c(Order1,Order2,Order3,Order4),
                                     avgValue),
                NUF=getNUF(c(Value1,Value2,Value3,Value4),medianValue),
                NUF2=getNUF(c(Value1,Value2,Value3,Value4),avgValue)) %>% ungroup()

df.or.rt.new.d.kept <- inner_join(df.or.rt.new.d,df.rating.new.d,by='participant') %>% rowwise() %>%
  dplyr::mutate(valueKept = getMeanUnChosen(c(Value1,Value2,Value3,Value4),
                                          c(Order1,Order2,Order3,Order4)),
                minKept=getMinUnChosen(c(Value1,Value2,Value3,Value4),
                                     c(Order1,Order2,Order3,Order4)),
                NUFKept=getNUFUnChosen(c(Value1,Value2,Value3,Value4),
                                     c(Order1,Order2,Order3,Order4),
                                     medianValue),
                NUFKept2=getNUFUnChosen(c(Value1,Value2,Value3,Value4),
                                     c(Order1,Order2,Order3,Order4),
                                     avgValue),
                NUF=getNUF(c(Value1,Value2,Value3,Value4),medianValue),
                NUF2=getNUF(c(Value1,Value2,Value3,Value4),avgValue)) %>% ungroup()

df.d.combined.or <- rbind(df.or.rt.3.kept %>% select(minKept,valueKept,NUFKept,NChosen,NUFKept2,NUF,NUF2,conflict,meanValue,medianValue,valueDiff,trialN,firstRT,acc,participant) %>% mutate(study='old'),
                          df.or.rt.new.d.kept %>% filter(firstRT<15) %>% select(minKept,valueKept,NUFKept,NChosen,NUFKept2,NUF,NUF2,conflict,meanValue,medianValue,valueDiff,trialN,firstRT,acc,participant) %>% mutate(study='new')) %>% ungroup() %>%
  dplyr::mutate(scaledMeanValue=scale(meanValue),
         scaledValueDiff=scale(valueDiff),
         scaledTrialNum=scale(trialN),
         scaledFirstRT=scale(firstRT),
         scaledConflict=scale(conflict),
         scaledNUF=scale(NUF),
         scaledNUF2=scale(NUF2),
         NRemain = 4 - NChosen,
         NRemain2 = if_else(NChosen<4,4 - NChosen,1),
         study=factor(study))

contrasts(df.d.combined.or$acc)<-contr.sum
contrasts(df.d.combined.or$study)<-contr.sum

model.N.s.combined.01 <- lmer(NChosen ~ study * (scaledConflict + poly(scaledMeanValue,2) + scaledTrialNum + scaledValueDiff + scaledFirstRT + acc) + (1 + scaledConflict + poly(scaledMeanValue,2) + scaledTrialNum + scaledValueDiff + scaledFirstRT + acc|participant),data=df.s.combined.or,REML=F)

## boundary (singular) fit: see help('isSingular')

model.N.d.combined.01 <- lmer(NChosen ~ study * (scaledConflict + poly(scaledMeanValue,2) + scaledTrialNum + scaledValueDiff + scaledFirstRT + acc) + (1 + scaledConflict + poly(scaledMeanValue,2) + scaledTrialNum + scaledValueDiff + scaledFirstRT + acc|participant),data=df.d.combined.or,REML=F)

## boundary (singular) fit: see help('isSingular')

model.NR.d.combined.01 <- lmer(NRemain ~ study * (scaledConflict + poly(scaledMeanValue,2) + scaledTrialNum + scaledValueDiff + scaledFirstRT + acc) + (1 + scaledConflict + poly(scaledMeanValue,2) + scaledTrialNum + scaledValueDiff + scaledFirstRT + acc|participant),data=df.d.combined.or,REML=F)

## boundary (singular) fit: see help('isSingular')

polymv <- poly(df.s.combined.or$scaledMeanValue,2)

df.s.combined.or$mvL <-polymv[,1]
df.s.combined.or$mvQ <-polymv[,2]

model.N.s.combined.01.direct <- lmer(NChosen ~ study * (scaledConflict + mvL + mvQ + scaledTrialNum + scaledValueDiff + scaledFirstRT + acc) + (1 + scaledConflict + mvL + mvQ + scaledTrialNum + scaledValueDiff + scaledFirstRT + acc|participant),data=df.s.combined.or,REML=F)

## boundary (singular) fit: see help('isSingular')

model.nuf.s.combined.ni.01.direct <- lmer(NUFKept2/NChosen ~ study * (scaledConflict + scaledNUF2 + mvL + mvQ + scaledTrialNum + scaledValueDiff + scaledFirstRT + acc) + (1 + scaledConflict + scaledNUF2 + mvL + mvQ + scaledTrialNum + scaledValueDiff + scaledFirstRT + acc|participant),data=df.s.combined.or,REML=F)

## boundary (singular) fit: see help('isSingular')

model.nuf.s.combined.ni.01.poly <- lmer(NUFKept2/NChosen ~ study * (scaledConflict + scaledNUF2 + poly(scaledMeanValue,2) + scaledTrialNum + scaledValueDiff + scaledFirstRT + acc) + (1 + scaledConflict + scaledNUF2 + poly(scaledMeanValue,2) + scaledTrialNum + scaledValueDiff + scaledFirstRT + acc|participant),data=df.s.combined.or,REML=F)

## boundary (singular) fit: see help('isSingular')

model.N.s.combined.01.poly <- lmer(NChosen ~ study * (scaledConflict + poly(scaledMeanValue,2) + scaledTrialNum + scaledValueDiff + scaledFirstRT + acc) + (1 + scaledConflict + poly(scaledMeanValue,2) + scaledTrialNum + scaledValueDiff + scaledFirstRT + acc|participant),data=df.s.combined.or,REML=F)

## boundary (singular) fit: see help('isSingular')

polymv <- poly(df.d.combined.or$scaledMeanValue,2)

df.d.combined.or$mvL <-polymv[,1]
df.d.combined.or$mvQ <-polymv[,2]

model.N.d.combined.01.direct <- lmer(NChosen ~ study * (scaledConflict + mvL + mvQ + scaledTrialNum + scaledValueDiff + scaledFirstRT + acc) + (1 + scaledConflict + mvL + mvQ + scaledTrialNum + scaledValueDiff + scaledFirstRT + acc|participant),data=df.d.combined.or,REML=F)

## boundary (singular) fit: see help('isSingular')

model.NR.d.combined.01.direct <- lmer(NRemain ~ study * (scaledConflict + mvL + mvQ + scaledTrialNum + scaledValueDiff + scaledFirstRT + acc) + (1 + scaledConflict + mvL + mvQ + scaledTrialNum + scaledValueDiff + scaledFirstRT + acc|participant),data=df.d.combined.or,REML=F)

## boundary (singular) fit: see help('isSingular')

model.nuf.d.combined.ni.01.direct <- lmer(NUFKept2/NRemain2 ~ study * (scaledConflict + scaledNUF2 + mvL + mvQ + scaledTrialNum + scaledValueDiff + scaledFirstRT + acc) + (1 + scaledConflict + scaledNUF2 + mvL + mvQ + scaledTrialNum + scaledValueDiff + scaledFirstRT + acc|participant),data=df.d.combined.or,REML=F)

## boundary (singular) fit: see help('isSingular')

model.nuf.d.combined.ni.01.poly <- lmer(NUFKept2/NRemain2 ~ study * (scaledConflict + scaledNUF2 + poly(scaledMeanValue,2) + scaledTrialNum + scaledValueDiff + scaledFirstRT + acc) + (1 + scaledConflict + scaledNUF2 + poly(scaledMeanValue,2) + scaledTrialNum + scaledValueDiff + scaledFirstRT + acc|participant),data=df.d.combined.or,REML=F)

## boundary (singular) fit: see help('isSingular')

model.N.d.combined.01.poly <- lmer(NChosen ~ study * (scaledConflict + poly(scaledMeanValue,2) + scaledTrialNum + scaledValueDiff + scaledFirstRT + acc) + (1 + scaledConflict + poly(scaledMeanValue,2) + scaledTrialNum + scaledValueDiff + scaledFirstRT + acc|participant),data=df.d.combined.or,REML=F)

## boundary (singular) fit: see help('isSingular')

df.all.combined.or.gr <- rbind(df.s.combined.or %>% mutate(NUFRatio=NUFKept2/NChosen,
                                                           NKept=NChosen) %>% select(NUFRatio,NUF2,NKept,conflict,meanValue,valueDiff,trialN,firstRT,acc,participant,scaledConflict,scaledMeanValue,scaledValueDiff,scaledFirstRT,scaledTrialNum,study,scaledNUF2) %>% mutate(action='s'),
                               df.d.combined.or %>% mutate(NUFRatio=NUFKept2/NRemain2,
                                                           NKept=NRemain) %>% 
select(NUFRatio,NUF2,NKept,conflict,meanValue,valueDiff,trialN,firstRT,acc,participant,scaledConflict,scaledMeanValue,scaledValueDiff,scaledFirstRT,scaledTrialNum,study,scaledNUF2) %>% mutate(action='r')) %>% mutate(action=factor(action)) %>%
  mutate(study=factor(study),
         scaledConflict=scale(conflict),
         scaledMeanValue=scale(meanValue),
         scaledValueDiff=scale(valueDiff),
         scaledTrialNum=scale(trialN),
         scaledFirstRT=scale(firstRT),
         scaledNUF2=scale(NUF2))

contrasts(df.all.combined.or.gr$acc)<-contr.sum
contrasts(df.all.combined.or.gr$study)<-contr.sum
contrasts(df.all.combined.or.gr$action)<-contr.sum

model.N.all.combined<- lmer(NKept ~ study * action * (scaledConflict + poly(scaledMeanValue,2) + scaledTrialNum + scaledValueDiff + scaledFirstRT + acc) + (1 + scaledConflict + poly(scaledMeanValue,2) + scaledTrialNum + scaledValueDiff + scaledFirstRT + acc|participant),data=df.all.combined.or.gr)

## boundary (singular) fit: see help('isSingular')

model.nuf.all.combined.ni<- lmer(NUFRatio ~ study * action * (scaledConflict + scaledNUF2 + poly(scaledMeanValue,2) + scaledTrialNum + scaledValueDiff + scaledFirstRT + acc) + (1 + scaledConflict + scaledNUF2 + poly(scaledMeanValue,2) + scaledTrialNum + scaledValueDiff + scaledFirstRT + acc|participant),data=df.all.combined.or.gr)

## boundary (singular) fit: see help('isSingular')

library(kableExtra)

## 
## Attaching package: 'kableExtra'

## The following object is masked from 'package:dplyr':
## 
##     group_rows

kbl(car::Anova(model.N.s.combined.01.poly,type="III"),digits = 3) %>%
  kable_classic(full_width = F, html_font = "Cambria")

	Chisq	Df	Pr(>Chisq)
(Intercept)	1766.405	1	0.000
study	0.040	1	0.841
scaledConflict	4.103	1	0.043
poly(scaledMeanValue, 2)	391.693	2	0.000
scaledTrialNum	2.295	1	0.130
scaledValueDiff	20.285	1	0.000
scaledFirstRT	60.274	1	0.000
acc	17.957	1	0.000
study:scaledConflict	0.074	1	0.785
study:poly(scaledMeanValue, 2)	3.370	2	0.185
study:scaledTrialNum	0.682	1	0.409
study:scaledValueDiff	0.000	1	0.984
study:scaledFirstRT	32.757	1	0.000
study:acc	0.686	1	0.408

kbl(car::Anova(model.N.d.combined.01.poly,type="III"),digits = 3) %>%
  kable_classic(full_width = F, html_font = "Cambria")

	Chisq	Df	Pr(>Chisq)
(Intercept)	3134.507	1	0.000
study	5.506	1	0.019
scaledConflict	30.216	1	0.000
poly(scaledMeanValue, 2)	395.738	2	0.000
scaledTrialNum	0.576	1	0.448
scaledValueDiff	8.585	1	0.003
scaledFirstRT	182.101	1	0.000
acc	0.470	1	0.493
study:scaledConflict	1.397	1	0.237
study:poly(scaledMeanValue, 2)	2.413	2	0.299
study:scaledTrialNum	1.396	1	0.237
study:scaledValueDiff	0.079	1	0.778
study:scaledFirstRT	71.691	1	0.000
study:acc	25.813	1	0.000

kbl(car::Anova(model.nuf.s.combined.ni.01.poly,type="III"),digits = 3) %>%
  kable_classic(full_width = F, html_font = "Cambria")

	Chisq	Df	Pr(>Chisq)
(Intercept)	2892.356	1	0.000
study	2.639	1	0.104
scaledConflict	7.240	1	0.007
scaledNUF2	4263.954	1	0.000
poly(scaledMeanValue, 2)	22.267	2	0.000
scaledTrialNum	4.818	1	0.028
scaledValueDiff	274.512	1	0.000
scaledFirstRT	2.402	1	0.121
acc	109.606	1	0.000
study:scaledConflict	1.386	1	0.239
study:scaledNUF2	0.001	1	0.971
study:poly(scaledMeanValue, 2)	5.415	2	0.067
study:scaledTrialNum	4.986	1	0.026
study:scaledValueDiff	6.652	1	0.010
study:scaledFirstRT	1.251	1	0.263
study:acc	0.604	1	0.437

kbl(car::Anova(model.nuf.d.combined.ni.01.poly,type="III"),digits = 3) %>%
  kable_classic(full_width = F, html_font = "Cambria")

	Chisq	Df	Pr(>Chisq)
(Intercept)	1628.943	1	0.000
study	4.915	1	0.027
scaledConflict	10.977	1	0.001
scaledNUF2	3311.947	1	0.000
poly(scaledMeanValue, 2)	107.874	2	0.000
scaledTrialNum	2.801	1	0.094
scaledValueDiff	293.749	1	0.000
scaledFirstRT	23.018	1	0.000
acc	7.891	1	0.005
study:scaledConflict	1.201	1	0.273
study:scaledNUF2	0.518	1	0.472
study:poly(scaledMeanValue, 2)	0.471	2	0.790
study:scaledTrialNum	2.264	1	0.132
study:scaledValueDiff	0.471	1	0.493
study:scaledFirstRT	14.911	1	0.000
study:acc	126.357	1	0.000

kbl(car::Anova(model.N.all.combined,type="III"),digits = 3) %>%
  kable_classic(full_width = F, html_font = "Cambria")

	Chisq	Df	Pr(>Chisq)
(Intercept)	4825.819	1	0.000
study	2.941	1	0.086
action	17.878	1	0.000
scaledConflict	29.611	1	0.000
poly(scaledMeanValue, 2)	731.735	2	0.000
scaledTrialNum	3.205	1	0.073
scaledValueDiff	4.165	1	0.041
scaledFirstRT	0.267	1	0.605
acc	7.609	1	0.006
study:action	0.279	1	0.597
study:scaledConflict	0.945	1	0.331
study:poly(scaledMeanValue, 2)	5.091	2	0.078
study:scaledTrialNum	2.073	1	0.150
study:scaledValueDiff	0.035	1	0.852
study:scaledFirstRT	0.936	1	0.333
study:acc	8.352	1	0.004
action:scaledConflict	4.146	1	0.042
action:poly(scaledMeanValue, 2)	67.886	2	0.000
action:scaledTrialNum	3.118	1	0.077
action:scaledValueDiff	48.953	1	0.000
action:scaledFirstRT	200.528	1	0.000
action:acc	12.224	1	0.000
study:action:scaledConflict	0.265	1	0.607
study:action:poly(scaledMeanValue, 2)	1.294	2	0.524
study:action:scaledTrialNum	0.580	1	0.446
study:action:scaledValueDiff	0.409	1	0.522
study:action:scaledFirstRT	106.539	1	0.000
study:action:acc	15.027	1	0.000

kbl(car::Anova(model.nuf.all.combined.ni,type="III"),digits = 3) %>%
  kable_classic(full_width = F, html_font = "Cambria")

	Chisq	Df	Pr(>Chisq)
(Intercept)	3642.579	1	0.000
study	3.490	1	0.062
action	21.406	1	0.000
scaledConflict	20.623	1	0.000
scaledNUF2	5237.155	1	0.000
poly(scaledMeanValue, 2)	55.682	2	0.000
scaledTrialNum	8.076	1	0.004
scaledValueDiff	565.062	1	0.000
scaledFirstRT	21.381	1	0.000
acc	41.776	1	0.000
study:action	4.672	1	0.031
study:scaledConflict	0.114	1	0.735
study:scaledNUF2	1.661	1	0.197
study:poly(scaledMeanValue, 2)	2.197	2	0.333
study:scaledTrialNum	5.862	1	0.015
study:scaledValueDiff	7.731	1	0.005
study:scaledFirstRT	2.630	1	0.105
study:acc	37.392	1	0.000
action:scaledConflict	1.143	1	0.285
action:scaledNUF2	2.372	1	0.124
action:poly(scaledMeanValue, 2)	140.836	2	0.000
action:scaledTrialNum	0.041	1	0.839
action:scaledValueDiff	11.899	1	0.001
action:scaledFirstRT	6.212	1	0.013
action:acc	105.693	1	0.000
study:action:scaledConflict	2.427	1	0.119
study:action:scaledNUF2	0.449	1	0.503
study:action:poly(scaledMeanValue, 2)	0.064	2	0.969
study:action:scaledTrialNum	0.027	1	0.870
study:action:scaledValueDiff	3.954	1	0.047
study:action:scaledFirstRT	13.022	1	0.000
study:action:acc	55.284	1	0.000

tab_model(model.N.s.combined.01,model.N.d.combined.01,model.NR.d.combined.01,model.N.all.combined,digits=3)

	NChosen			NChosen			NRemain			NKept
Predictors	Estimates	CI	p	Estimates	CI	p	Estimates	CI	p	Estimates	CI	p
(Intercept)	2.277	2.170 – 2.383	<0.001	1.873	1.807 – 1.938	<0.001	2.127	2.061 – 2.193	<0.001	2.200	2.138 – 2.262	<0.001
study1	0.011	-0.095 – 0.117	0.841	-0.078	-0.144 – -0.013	0.019	0.078	0.013 – 0.144	0.019	0.054	-0.008 – 0.116	0.086
scaledConflict	0.023	0.001 – 0.045	0.043	-0.051	-0.069 – -0.033	<0.001	0.050	0.032 – 0.068	<0.001	0.037	0.024 – 0.051	<0.001
scaledMeanValue [1st degree]	49.107	44.243 – 53.971	<0.001	-47.806	-52.565 – -43.047	<0.001	47.837	43.077 – 52.597	<0.001	68.247	63.302 – 73.193	<0.001
scaledMeanValue [2nd degree]	6.175	3.087 – 9.264	<0.001	10.830	8.515 – 13.144	<0.001	-10.819	-13.124 – -8.514	<0.001	-2.905	-5.691 – -0.118	0.041
scaledTrialNum	0.021	-0.006 – 0.048	0.130	-0.008	-0.028 – 0.012	0.448	0.008	-0.012 – 0.028	0.446	0.015	-0.001 – 0.032	0.073
scaledValueDiff	-0.056	-0.081 – -0.032	<0.001	-0.027	-0.045 – -0.009	0.003	0.027	0.009 – 0.045	0.003	-0.015	-0.030 – -0.001	0.041
scaledFirstRT	-0.118	-0.148 – -0.088	<0.001	-0.129	-0.147 – -0.110	<0.001	0.129	0.110 – 0.147	<0.001	0.005	-0.013 – 0.022	0.605
acc1	0.038	0.020 – 0.055	<0.001	0.006	-0.011 – 0.022	0.493	-0.006	-0.022 – 0.011	0.493	0.017	0.005 – 0.029	0.006
study1 × scaledConflict	0.003	-0.019 – 0.025	0.785	-0.011	-0.029 – 0.007	0.237	0.011	-0.007 – 0.029	0.235	0.007	-0.007 – 0.020	0.331
study1 × scaledMeanValue [1st degree]	4.174	-0.690 – 9.039	0.093	-3.752	-8.511 – 1.007	0.122	3.757	-1.003 – 8.517	0.122	5.324	0.378 – 10.269	0.035
study1 × scaledMeanValue [2nd degree]	-0.647	-3.735 – 2.442	0.682	0.778	-1.536 – 3.092	0.510	-0.778	-3.082 – 1.527	0.508	-1.382	-4.169 – 1.405	0.331
study1 × scaledTrialNum	0.011	-0.016 – 0.039	0.409	-0.012	-0.032 – 0.008	0.237	0.012	-0.008 – 0.032	0.237	0.012	-0.004 – 0.029	0.150
study1 × scaledValueDiff	0.000	-0.024 – 0.025	0.984	0.003	-0.015 – 0.021	0.778	-0.003	-0.021 – 0.015	0.783	-0.001	-0.016 – 0.013	0.852
study1 × scaledFirstRT	0.087	0.057 – 0.117	<0.001	0.081	0.062 – 0.099	<0.001	-0.081	-0.099 – -0.062	<0.001	0.009	-0.009 – 0.026	0.333
study1 × acc1	0.007	-0.010 – 0.025	0.408	0.042	0.026 – 0.059	<0.001	-0.042	-0.058 – -0.026	<0.001	-0.018	-0.030 – -0.006	0.004
action1										-0.096	-0.140 – -0.051	<0.001
study1 × action1										0.012	-0.032 – 0.056	0.597
action1 × scaledConflict										0.014	0.001 – 0.027	0.042
action1 × scaledMeanValue [1st degree]										-4.280	-8.455 – -0.106	0.044
action1 × scaledMeanValue [2nd degree]										-10.010	-12.541 – -7.479	<0.001
action1 × scaledTrialNum										-0.014	-0.030 – 0.002	0.077
action1 × scaledValueDiff										0.049	0.035 – 0.062	<0.001
action1 × scaledFirstRT										0.119	0.103 – 0.136	<0.001
action1 × acc1										-0.021	-0.033 – -0.009	<0.001
(study1 × action1) × scaledConflict										0.003	-0.010 – 0.017	0.607
(study1 × action1) × scaledMeanValue [1st degree]										-1.291	-5.466 – 2.883	0.544
(study1 × action1) × scaledMeanValue [2nd degree]										1.315	-1.217 – 3.846	0.309
(study1 × action1) × scaledTrialNum										-0.006	-0.022 – 0.010	0.446
(study1 × action1) × scaledValueDiff										0.004	-0.009 – 0.018	0.522
(study1 × action1) × scaledFirstRT										-0.087	-0.103 – -0.070	<0.001
study1 × action1 × acc1										-0.023	-0.035 – -0.012	<0.001
Random Effects
σ2	0.40			0.36			0.36			0.38
τ00	0.39 participant			0.15 participant			0.15 participant			0.26 participant
τ11	0.00 participant.scaledConflict			0.00 participant.scaledConflict			0.00 participant.scaledConflict			0.00 participant.scaledConflict
	710.22 participant.poly(scaledMeanValue, 2)1			729.52 participant.poly(scaledMeanValue, 2)1			730.20 participant.poly(scaledMeanValue, 2)1			1481.47 participant.poly(scaledMeanValue, 2)1
	201.89 participant.poly(scaledMeanValue, 2)2			78.14 participant.poly(scaledMeanValue, 2)2			76.60 participant.poly(scaledMeanValue, 2)2			286.16 participant.poly(scaledMeanValue, 2)2
	0.02 participant.scaledTrialNum			0.01 participant.scaledTrialNum			0.01 participant.scaledTrialNum			0.01 participant.scaledTrialNum
	0.01 participant.scaledValueDiff			0.00 participant.scaledValueDiff			0.00 participant.scaledValueDiff			0.00 participant.scaledValueDiff
	0.02 participant.scaledFirstRT			0.00 participant.scaledFirstRT			0.00 participant.scaledFirstRT			0.01 participant.scaledFirstRT
	0.00 participant.acc1			0.00 participant.acc1			0.00 participant.acc1			0.00 participant.acc1
ρ01	-0.02			-0.74			-0.80			-0.37
	0.19			-0.35			-0.35			-0.04
	-0.67			-0.45			-0.46			-0.69
	0.25			0.36			0.36			0.29
	-0.73			-0.92			-0.92			-0.93
	-0.29			-0.73			-0.73			-0.43
	-0.20			0.34			0.41			-0.18
ICC				0.42
N	141 participant			159 participant			159 participant			294 participant
Observations	8587			9349			9349			17936
Marginal R2 / Conditional R2	0.467 / NA			0.350 / 0.624			0.482 / NA			0.478 / NA

tab_model(model.nuf.s.combined.ni.01.direct,model.nuf.d.combined.ni.01.direct,digits=3)

	NUFKept2/NChosen			NUFKept2/NRemain2
Predictors	Estimates	CI	p	Estimates	CI	p
(Intercept)	0.285	0.275 – 0.296	<0.001	0.322	0.306 – 0.338	<0.001
study1	-0.009	-0.019 – 0.002	0.104	-0.018	-0.033 – -0.002	0.027
scaledConflict	0.007	0.002 – 0.013	0.007	0.011	0.004 – 0.017	0.001
scaledNUF2	0.342	0.332 – 0.352	<0.001	0.352	0.340 – 0.364	<0.001
mvL	-0.498	-1.286 – 0.289	0.215	9.395	7.518 – 11.273	<0.001
mvQ	1.442	0.839 – 2.045	<0.001	-4.331	-5.290 – -3.372	<0.001
scaledTrialNum	0.005	0.001 – 0.010	0.028	0.005	-0.001 – 0.012	0.094
scaledValueDiff	-0.082	-0.092 – -0.073	<0.001	-0.056	-0.062 – -0.050	<0.001
scaledFirstRT	0.005	-0.001 – 0.010	0.121	0.014	0.008 – 0.020	<0.001
acc1	0.048	0.039 – 0.057	<0.001	-0.010	-0.018 – -0.003	0.005
study1 × scaledConflict	-0.003	-0.009 – 0.002	0.239	0.003	-0.003 – 0.010	0.273
study1 × scaledNUF2	-0.000	-0.010 – 0.010	0.971	0.004	-0.008 – 0.016	0.472
study1 × mvL	-0.728	-1.516 – 0.060	0.070	-0.524	-2.402 – 1.353	0.584
study1 × mvQ	0.530	-0.073 – 1.133	0.085	0.326	-0.633 – 1.286	0.505
study1 × scaledTrialNum	0.005	0.001 – 0.010	0.026	0.005	-0.001 – 0.011	0.132
study1 × scaledValueDiff	-0.013	-0.023 – -0.003	0.010	-0.002	-0.009 – 0.004	0.493
study1 × scaledFirstRT	0.003	-0.002 – 0.009	0.263	-0.012	-0.017 – -0.006	<0.001
study1 × acc1	-0.004	-0.013 – 0.005	0.437	0.041	0.034 – 0.049	<0.001
Random Effects
σ2	0.03			0.06
τ00	0.00 participant			0.01 participant
τ11	0.00 participant.scaledConflict			0.00 participant.scaledConflict
	0.00 participant.scaledNUF2			0.00 participant.scaledNUF2
	1.05 participant.mvL			72.46 participant.mvL
	4.85 participant.mvQ			17.54 participant.mvQ
	0.00 participant.scaledTrialNum			0.00 participant.scaledTrialNum
	0.00 participant.scaledValueDiff			0.00 participant.scaledValueDiff
	0.00 participant.scaledFirstRT			0.00 participant.scaledFirstRT
	0.00 participant.acc1			0.00 participant.acc1
ρ01	-0.34			-0.97
	0.56			0.57
	0.98			-0.74
	-0.72			0.62
	0.08			0.31
	0.72			-0.13
	-0.40			-0.75
	-0.39			0.02
N	141 participant			159 participant
Observations	8587			9349
Marginal R2 / Conditional R2	0.799 / NA			0.600 / NA

tab_model(model.nuf.all.combined.ni,digits=3)

	NUFRatio
Predictors	Estimates	CI	p
(Intercept)	0.303	0.293 – 0.313	<0.001
study1	-0.009	-0.019 – 0.000	0.062
action1	-0.020	-0.028 – -0.011	<0.001
scaledConflict	0.009	0.005 – 0.013	<0.001
scaledNUF2	0.344	0.335 – 0.354	<0.001
scaledMeanValue [1st degree]	5.409	3.987 – 6.830	<0.001
scaledMeanValue [2nd degree]	-1.875	-2.714 – -1.037	<0.001
scaledTrialNum	0.006	0.002 – 0.010	0.004
scaledValueDiff	-0.069	-0.074 – -0.063	<0.001
scaledFirstRT	0.010	0.006 – 0.014	<0.001
acc1	0.020	0.014 – 0.026	<0.001
study1 × action1	-0.009	-0.018 – -0.001	0.031
study1 × scaledConflict	0.001	-0.003 – 0.005	0.735
study1 × scaledNUF2	0.006	-0.003 – 0.015	0.197
study1 × scaledMeanValue [1st degree]	-0.736	-2.158 – 0.685	0.310
study1 × scaledMeanValue [2nd degree]	0.625	-0.213 – 1.463	0.144
study1 × scaledTrialNum	0.005	0.001 – 0.009	0.015
study1 × scaledValueDiff	-0.008	-0.014 – -0.002	0.005
study1 × scaledFirstRT	-0.003	-0.008 – 0.001	0.105
study1 × acc1	0.019	0.013 – 0.025	<0.001
action1 × scaledConflict	0.002	-0.002 – 0.006	0.285
action1 × scaledNUF2	0.007	-0.002 – 0.015	0.124
action1 × scaledMeanValue [1st degree]	7.191	5.852 – 8.530	<0.001
action1 × scaledMeanValue [2nd degree]	-4.118	-4.916 – -3.319	<0.001
action1 × scaledTrialNum	-0.000	-0.004 – 0.004	0.839
action1 × scaledValueDiff	0.010	0.004 – 0.015	0.001
action1 × scaledFirstRT	0.005	0.001 – 0.009	0.013
action1 × acc1	-0.030	-0.035 – -0.024	<0.001
(study1 × action1) × scaledConflict	0.003	-0.001 – 0.007	0.119
(study1 × action1) × scaledNUF2	-0.003	-0.012 – 0.006	0.503
(study1 × action1) × scaledMeanValue [1st degree]	-0.100	-1.439 – 1.239	0.883
(study1 × action1) × scaledMeanValue [2nd degree]	-0.041	-0.840 – 0.758	0.920
(study1 × action1) × scaledTrialNum	-0.000	-0.004 – 0.004	0.870
(study1 × action1) × scaledValueDiff	0.006	0.000 – 0.011	0.047
(study1 × action1) × scaledFirstRT	-0.007	-0.011 – -0.003	<0.001
study1 × action1 × acc1	0.021	0.016 – 0.027	<0.001
Random Effects
σ2	0.04
τ00 participant	0.01
τ11 participant.scaledConflict	0.00
τ11 participant.scaledNUF2	0.00
τ11 participant.poly(scaledMeanValue, 2)1	58.67
τ11 participant.poly(scaledMeanValue, 2)2	22.53
τ11 participant.scaledTrialNum	0.00
τ11 participant.scaledValueDiff	0.00
τ11 participant.scaledFirstRT	0.00
τ11 participant.acc1	0.00
ρ01	-0.65
	0.64
	-0.46
	0.29
	0.28
	0.25
	-0.75
	-0.19
N participant	294
Observations	17936
Marginal R2 / Conditional R2	0.700 / NA

eff_vd.n.s.all <- Effect(c("scaledValueDiff"),
                   model.N.s.combined.01,
                   xlevels=list(scaledValueDiff=seq(min(quantile(df.s.combined.or$scaledValueDiff,0.025),
                                                        quantile(df.d.combined.or$scaledValueDiff,0.025)),
                                                    max(quantile(df.s.combined.or$scaledValueDiff,0.975),
                                                        quantile(df.d.combined.or$scaledValueDiff,0.975)),0.1)))

## Warning in Analyze.model(focal.predictors, mod, xlevels, default.levels, : the
## predictors scaledConflict, scaledTrialNum, scaledValueDiff, scaledFirstRT,
## scaledMeanValue are one-column matrices that were converted to vectors

IA.vd.N.s.all <- as.data.frame(eff_vd.n.s.all) %>% mutate(study='Selection')


eff_vd.n.d.all <- Effect(c("scaledValueDiff"),
                   model.N.d.combined.01,
                   xlevels=list(scaledValueDiff=seq(min(quantile(df.s.combined.or$scaledValueDiff,0.025),
                                                        quantile(df.d.combined.or$scaledValueDiff,0.025)),
                                                    max(quantile(df.s.combined.or$scaledValueDiff,0.975),
                                                        quantile(df.d.combined.or$scaledValueDiff,0.975)),0.1)))

## Warning in Analyze.model(focal.predictors, mod, xlevels, default.levels, : the
## predictors scaledConflict, scaledTrialNum, scaledValueDiff, scaledFirstRT,
## scaledMeanValue are one-column matrices that were converted to vectors

IA.vd.N.d.all <- as.data.frame(eff_vd.n.d.all) %>% mutate(study='Removal')

IA.vd.N.all <- rbind(IA.vd.N.s.all,IA.vd.N.d.all)

p.eff.vd.N.all<-ggplot(data=IA.vd.N.all, aes(x=scaledValueDiff, y=fit, group=study)) +
  geom_line(size=0.5,aes(color=study))+theme_bw(12) +
  geom_ribbon(data=IA.vd.N.all, aes(x=scaledValueDiff, max = upper, min = lower,fill=study),alpha=0.3, inherit.aes = FALSE)+ 
  xlab("Relative Value\n(z-scored)") + ylab("N Chosen") + 
  theme(panel.border = element_blank(), panel.grid.major = element_blank(), 
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),
        axis.ticks = element_line(colour = "black",size=0.2),
        axis.title.y.right = element_text(color = '#AA0000', size=6)) +
  theme(legend.justification=c(1,1),legend.position='none',text = element_text(size=6)) + 
  scale_fill_manual("",values=c('#AA0000','#222222')) + 
  scale_color_manual("",values=c('#AA0000','#222222')) + 
  coord_cartesian(ylim=c(1.5,2.5)) +   scale_y_continuous(
    name = "N Chosen",
    breaks = c(1.5,2.5),
    sec.axis = sec_axis(~.*1, name="N Removed",breaks=c(1.5,2.5))
  )
p.eff.vd.N.all

eff_mv.n.s.all <- Effect(c("scaledMeanValue"),
                   model.N.s.combined.01,
                   xlevels=list(scaledMeanValue=seq(min(quantile(df.s.combined.or$scaledMeanValue,0.025),
                                                        quantile(df.d.combined.or$scaledMeanValue,0.025)),
                                                    max(quantile(df.s.combined.or$scaledMeanValue,0.975),
                                                        quantile(df.d.combined.or$scaledMeanValue,0.975)),0.1)))

## Warning in Analyze.model(focal.predictors, mod, xlevels, default.levels, : the
## predictors scaledConflict, scaledTrialNum, scaledValueDiff, scaledFirstRT,
## scaledMeanValue are one-column matrices that were converted to vectors

IA.mv.N.s.all <- as.data.frame(eff_mv.n.s.all) %>% mutate(study='Selection')


eff_mv.n.d.all <- Effect(c("scaledMeanValue"),
                   model.N.d.combined.01,
                   xlevels=list(scaledMeanValue=seq(min(quantile(df.s.combined.or$scaledMeanValue,0.025),
                                                        quantile(df.d.combined.or$scaledMeanValue,0.025)),
                                                    max(quantile(df.s.combined.or$scaledMeanValue,0.975),
                                                        quantile(df.d.combined.or$scaledMeanValue,0.975)),0.1)))

## Warning in Analyze.model(focal.predictors, mod, xlevels, default.levels, : the
## predictors scaledConflict, scaledTrialNum, scaledValueDiff, scaledFirstRT,
## scaledMeanValue are one-column matrices that were converted to vectors

IA.mv.N.d.all <- as.data.frame(eff_mv.n.d.all) %>% mutate(study='Removal')

IA.mv.N.all <- rbind(IA.mv.N.s.all,IA.mv.N.d.all)

p.eff.mv.N.all<-ggplot(data=IA.mv.N.all, aes(x=scaledMeanValue, y=fit, group=study)) +
  geom_line(size=0.5,aes(color=study))+theme_bw(12) +
  geom_ribbon(data=IA.mv.N.all, aes(x=scaledMeanValue, max = upper, min = lower,fill=study),alpha=0.3, inherit.aes = FALSE)+ 
  xlab("Overall Value\n(z-scored)") + ylab("N Chosen") + 
  theme(panel.border = element_blank(), panel.grid.major = element_blank(), 
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),
        axis.ticks = element_line(colour = "black",size=0.2),
        axis.title.y.right = element_text(color = '#AA0000', size=6)) +
  theme(legend.justification=c(1,1),legend.position='none',text = element_text(size=6)) + 
  scale_fill_manual("",values=c('#AA0000','#222222')) + 
  scale_color_manual("",values=c('#AA0000','#222222')) + 
  coord_cartesian(ylim=c(1,4)) +   scale_y_continuous(
    name = "N Chosen",
    breaks = c(1,4),
    sec.axis = sec_axis(~.*1, name="N Removed",breaks=c(1,4))
  )
p.eff.mv.N.all

eff_mv.nc.s <- Effect(c("scaledConflict"),
                   model.N.s.combined.01.direct,
                   xlevels=list(scaledConflict=seq(min(quantile(df.s.combined.or$scaledConflict,0.025),
                                                        quantile(df.d.combined.or$scaledConflict,0.025)),
                                                    max(quantile(df.s.combined.or$scaledConflict,0.975),
                                                        quantile(df.d.combined.or$scaledConflict,0.975)),0.1)))

## Warning in Analyze.model(focal.predictors, mod, xlevels, default.levels, : the
## predictors scaledConflict, scaledTrialNum, scaledValueDiff, scaledFirstRT are
## one-column matrices that were converted to vectors

IA.mv.nc.s <- as.data.frame(eff_mv.nc.s) %>% mutate(study='Selection')


eff_mv.nc.d <- Effect(c("scaledConflict"),
                   model.NR.d.combined.01.direct,
                   xlevels=list(scaledConflict=seq(min(quantile(df.s.combined.or$scaledConflict,0.025),
                                                        quantile(df.d.combined.or$scaledConflict,0.025)),
                                                    max(quantile(df.s.combined.or$scaledConflict,0.975),
                                                        quantile(df.d.combined.or$scaledConflict,0.975)),0.1)))

## Warning in Analyze.model(focal.predictors, mod, xlevels, default.levels, : the
## predictors scaledConflict, scaledTrialNum, scaledValueDiff, scaledFirstRT are
## one-column matrices that were converted to vectors

IA.mv.nc.d <- as.data.frame(eff_mv.nc.d) %>% mutate(study='Removal')

IA.mv.nc.t <- rbind(IA.mv.nc.s,IA.mv.nc.d) %>% mutate(study=relevel(factor(study),ref = 'Selection'))


test<-ggplot(data=IA.mv.nc.t, aes(x=scaledConflict, y=fit, group=study)) +
  geom_line(size=0.5,aes(color=study))+theme_bw(12) +
  geom_ribbon(data=IA.mv.nc.t, aes(x=scaledConflict, max = upper, min = lower,fill=study),alpha=0.3, inherit.aes = FALSE)+ 
  xlab("Conflict\n(z-scored)") + ylab("N Kept") + 
  theme(panel.border = element_blank(), panel.grid.major = element_blank(), 
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),
        axis.ticks = element_line(colour = "black",size=0.2)) +
  theme(legend.justification=c(1,1),legend.position = 'none',text = element_text(size=6)) + 
  scale_fill_manual("",values=c('#222222','#AA0000')) + 
  scale_color_manual("",values=c('#222222','#AA0000')) + 
  coord_cartesian(ylim=c(2,2.5)) + scale_y_continuous(breaks = c(2,2.5))
test

eff_mv.nc.s <- Effect(c("scaledConflict"),
                   model.nuf.s.combined.ni.01.direct,
                   xlevels=list(scaledConflict=seq(min(quantile(df.s.combined.or$scaledConflict,0.025),
                                                        quantile(df.d.combined.or$scaledConflict,0.025)),
                                                    max(quantile(df.s.combined.or$scaledConflict,0.975),
                                                        quantile(df.d.combined.or$scaledConflict,0.975)),0.1)))

## Warning in Analyze.model(focal.predictors, mod, xlevels, default.levels, : the
## predictors scaledConflict, scaledNUF2, scaledTrialNum, scaledValueDiff,
## scaledFirstRT are one-column matrices that were converted to vectors

IA.mv.nc.s <- as.data.frame(eff_mv.nc.s) %>% mutate(study='Selection')


eff_mv.nc.d <- Effect(c("scaledConflict"),
                   model.nuf.d.combined.ni.01.direct,
                   xlevels=list(scaledConflict=seq(min(quantile(df.s.combined.or$scaledConflict,0.025),
                                                        quantile(df.d.combined.or$scaledConflict,0.025)),
                                                    max(quantile(df.s.combined.or$scaledConflict,0.975),
                                                        quantile(df.d.combined.or$scaledConflict,0.975)),0.1)))

## Warning in Analyze.model(focal.predictors, mod, xlevels, default.levels, : the
## predictors scaledConflict, scaledNUF2, scaledTrialNum, scaledValueDiff,
## scaledFirstRT are one-column matrices that were converted to vectors

IA.mv.nc.d <- as.data.frame(eff_mv.nc.d) %>% mutate(study='Removal')

IA.mv.nc.t <- rbind(IA.mv.nc.s,IA.mv.nc.d) %>% mutate(study=relevel(factor(study),ref = 'Selection'))


test2<-ggplot(data=IA.mv.nc.t, aes(x=scaledConflict, y=fit, group=study)) +
  geom_line(size=0.5,aes(color=study))+theme_bw(12) +
  geom_ribbon(data=IA.mv.nc.t, aes(x=scaledConflict, max = upper, min = lower,fill=study),alpha=0.3, inherit.aes = FALSE)+ 
  xlab("Conflict\n(z-scored)") + ylab("P(Suboptimal)") + 
  theme(panel.border = element_blank(), panel.grid.major = element_blank(), 
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),
        axis.ticks = element_line(colour = "black",size=0.2)) +
  theme(legend.justification=c(1,1),legend.position = 'none',text = element_text(size=6)) + 
  scale_fill_manual("",values=c('#222222','#AA0000')) + 
  scale_color_manual("",values=c('#222222','#AA0000')) + 
  coord_cartesian(ylim=c(.2,.4)) + scale_y_continuous(breaks = c(.2,.4))
test2

df.value.12 <- gather(df.total.rt.12 %>% select(participant,trialN,Value1:Value4,meanValue,valueDiff,catChoiceCondition),
       'position','value',Value1:Value4)

df.order.12 <- gather(df.total.rt.12 %>% select(participant,trialN,Order1:Order4),
       'position','order',Order1:Order4)

df.value.12$order <- df.order.12$order

df.order.value.12 <- inner_join(df.value.12,rbind(df.rating.1.summary,df.rating.2.summary),by='participant')

df.value.ns <- gather(df.total.rt.new.s %>% select(participant,trialN,Value1:Value4,meanValue,valueDiff,catChoiceCondition),
       'position','value',Value1:Value4)

df.order.ns <- gather(df.total.rt.new.s %>% select(participant,trialN,Order1:Order4),
       'position','order',Order1:Order4)

df.value.ns$order <- df.order.ns$order

df.order.value.ns <- inner_join(df.value.ns,df.rating.new.s %>% select(participant,medianValue,avgValue),by='participant')

df.order.value.s <- rbind(df.order.value.12 %>% mutate(study='1'),df.order.value.ns %>% mutate(study='2')) %>% 
  filter(catChoiceCondition=='OR') %>%
  mutate(isOpt=factor(value>avgValue),
         isChosen=factor(order>0),
         order=factor(order),
         scaledMeanValue=scale(meanValue),
         scaledValueDiff=scale(valueDiff),
         scaledValue=scale(value),
         scaledAvgValue=scale(avgValue),
         scaledDevValue=scale(value-avgValue),
         study=factor(study))
contrasts(df.order.value.s$study)<-contr.sum


model.order.s <- glmer(isChosen ~ scaledMeanValue + scaledDevValue + (1 + scaledMeanValue + scaledDevValue |participant) + (1|study),data=df.order.value.s,
                     family=binomial())

summary(model.order.s)

## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: isChosen ~ scaledMeanValue + scaledDevValue + (1 + scaledMeanValue +  
##     scaledDevValue | participant) + (1 | study)
##    Data: df.order.value.s
## 
##      AIC      BIC   logLik deviance df.resid 
##  34332.9  34417.3 -17156.4  34312.9    34370 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -9.9147 -0.6174  0.1875  0.5924  7.7932 
## 
## Random effects:
##  Groups      Name            Variance Std.Dev. Corr       
##  participant (Intercept)     3.2990   1.8163              
##              scaledMeanValue 0.1667   0.4082    0.22      
##              scaledDevValue  0.8870   0.9418   -0.19 -0.80
##  study       (Intercept)     0.1752   0.4186              
## Number of obs: 34380, groups:  participant, 141; study, 2
## 
## Fixed effects:
##                 Estimate Std. Error z value Pr(>|z|)    
## (Intercept)      0.46587    0.33491   1.391    0.164    
## scaledMeanValue -0.80118    0.04671 -17.153   <2e-16 ***
## scaledDevValue   2.11210    0.08787  24.036   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) scldMV
## scaledMenVl  0.063       
## scaledDevVl -0.069 -0.756

df.value.3 <- gather(df.total.rt.3 %>% select(participant,trialN,Value1:Value4,meanValue,valueDiff,catChoiceCondition),
       'position','value',Value1:Value4)

df.order.3 <- gather(df.total.rt.3 %>% select(participant,trialN,Order1:Order4),
       'position','order',Order1:Order4)

df.value.3$order <- df.order.3$order

df.order.value.3 <- inner_join(df.value.3,df.rating.3.summary,by='participant')

df.value.newd <- gather(df.total.rt.new.d %>% select(participant,trialN,Value1:Value4,meanValue,valueDiff,catChoiceCondition),
       'position','value',Value1:Value4)

df.order.newd <- gather(df.total.rt.new.d %>% select(participant,trialN,Order1:Order4),
       'position','order',Order1:Order4)

df.value.newd$order <- df.order.newd$order

df.order.value.nd <- inner_join(df.value.newd,df.rating.new.d  %>% select(participant,medianValue,avgValue),by='participant')

df.order.value.d <- rbind(df.order.value.3 %>% mutate(study='1'),df.order.value.nd %>% mutate(study='2')) %>% 
  filter(catChoiceCondition=='OR') %>%
  mutate(isOpt=factor(value>avgValue),
         isChosen=factor(order>0),
         scaledMeanValue=scale(meanValue),
         scaledValueDiff=scale(valueDiff),
         scaledValue=scale(value),
         scaledAvgValue=scale(avgValue),
         scaledDevValue=scale(value-avgValue),
         study=factor(study))
contrasts(df.order.value.d$study)<-contr.sum


model.order.d <- glmer(isChosen ~ scaledMeanValue + scaledDevValue + (1 + scaledMeanValue + scaledDevValue |participant) + (1|study),data=df.order.value.d,
                     family=binomial())

summary(model.order.d)

## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: isChosen ~ scaledMeanValue + scaledDevValue + (1 + scaledMeanValue +  
##     scaledDevValue | participant) + (1 | study)
##    Data: df.order.value.d
## 
##      AIC      BIC   logLik deviance df.resid 
##  41748.1  41833.4 -20864.0  41728.1    37410 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -8.8007 -0.7063 -0.3027  0.7419  7.9274 
## 
## Random effects:
##  Groups      Name            Variance Std.Dev. Corr       
##  participant (Intercept)     0.6408   0.8005              
##              scaledMeanValue 0.1910   0.4370   -0.24      
##              scaledDevValue  0.7355   0.8576   -0.01 -0.90
##  study       (Intercept)     0.0118   0.1086              
## Number of obs: 37420, groups:  participant, 159; study, 2
## 
## Fixed effects:
##                 Estimate Std. Error z value Pr(>|z|)    
## (Intercept)     -0.19868    0.10243   -1.94   0.0524 .  
## scaledMeanValue  0.91615    0.04577   20.02   <2e-16 ***
## scaledDevValue  -1.75188    0.07390  -23.71   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) scldMV
## scaledMenVl -0.132       
## scaledDevVl  0.001 -0.836

rawDevValue <- seq(-5,5,0.1)

newscaledDevValue <- scale(rawDevValue,center = mean(df.order.value.d$value-df.order.value.d$avgValue),
                           scale = sd(df.order.value.d$value-df.order.value.d$avgValue))

df.effect.value.d <- data.frame(Effect(model.order.d,focal.predictors = c('scaledDevValue'),xlevels=list(scaledDevValue=newscaledDevValue)))

## Warning in Analyze.model(focal.predictors, mod, xlevels, default.levels, : the
## predictors scaledMeanValue, scaledDevValue are one-column matrices that were
## converted to vectors

df.effect.value.d$rawx <- rawDevValue

df.effect.value.d$study <- 'd'

newscaledDevValue <- scale(rawDevValue,center = mean(df.order.value.s$value-df.order.value.s$avgValue),
                           scale = sd(df.order.value.s$value-df.order.value.s$avgValue))

df.effect.value.s <- data.frame(Effect(model.order.s,focal.predictors = c('scaledDevValue'),xlevels=list(scaledDevValue=newscaledDevValue)))

## Warning in Analyze.model(focal.predictors, mod, xlevels, default.levels, : the
## predictors scaledMeanValue, scaledDevValue are one-column matrices that were
## converted to vectors

df.effect.value.s$rawx <- rawDevValue

df.effect.value.s$study <- 's'

df.effect.value <- rbind(df.effect.value.s,df.effect.value.d) %>% mutate(study=factor(study))

contrasts(df.effect.value$study) <- contr.sum

p.eff.vtr.N.all<-ggplot(data=df.effect.value, aes(x=rawx, y=fit, group=study)) +
  geom_line(size=0.5,aes(color=study))+theme_bw(12) +
  geom_ribbon(data=df.effect.value, aes(x=rawx, max = upper, min = lower,fill=study),alpha=0.3, inherit.aes = FALSE)+ 
  xlab("Item Value - Average") + ylab("P(Chosen)") + 
  theme(panel.border = element_blank(), panel.grid.major = element_blank(), 
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),
        axis.ticks = element_line(colour = "black",size=0.2),
        axis.title.y.right = element_text(color = '#AA0000', size=6)) +
  theme(legend.justification=c(1,1),legend.position='none',text = element_text(size=6)) + 
  scale_fill_manual("",values=c('#AA0000','#222222')) + 
  scale_color_manual("",values=c('#AA0000','#222222')) + 
  coord_cartesian(ylim=c(0,1)) +   scale_y_continuous(
    breaks = c(0,0.5,1),
    sec.axis = sec_axis(~.*1, name="P(Removed)",breaks=c(0,0.5,1))
  ) + geom_vline(xintercept = 0,size=0.2) + geom_hline(yintercept = 0.5,size=0.2)
p.eff.vtr.N.all

lay <- rbind(c(1,2,NA),c(1,2,3),c(4,5,3),c(4,5,NA))

plots <- list(p.eff.mv.N.all,p.eff.vd.N.all,p.eff.vtr.N.all,test,test2)
grobs <- list()
widths <- list()
heights <- list()

for (i in 1:length(plots)){
    grobs[[i]] <- ggplotGrob(plots[[i]])
    widths[[i]] <- grobs[[i]]$widths
    heights[[i]] <- grobs[[i]]$heights
}

maxwidth <- do.call(grid::unit.pmax, widths)
maxheight <- do.call(grid::unit.pmax,heights)

for (i in 1:length(grobs)){
     grobs[[i]]$heights <- as.list(maxheight)
     grobs[[i]]$widths <- as.list(maxwidth)
}

p<-grid.arrange(grobs = grobs, layout_matrix = lay,widths=unit(c(3.6,3.6,3.6), c("cm", "cm")),heights=unit(c(1.5,1.5,1.5,1.5),c('cm')))

ggsave(filename = '../Figures/Figure9_V3.pdf',p,units = 'cm',width = 18,height = 10)

df.rating.ddl <- read.csv('../Data/Study4/Study4_2.csv')

df.total.ddl <- read.csv('../Data/Study4/Study4_1.csv') %>%
  mutate(catChoiceCondition=relevel(factor(duration),ref='60'),
         isBestFirst=firstValue==bestValue,
         scaledMeanValue=scale(meanValue),
         scaledValueDiff=scale(valueDiff),
         scaledTrialNum=scale(trialN))

df.total.rt.ddl <- df.total.ddl %>% 
  mutate(catChoiceCondition=relevel(factor(duration),ref='60'),
         rr=firstValue/firstRT) %>% filter(firstRT>0.1,firstRT<15) %>%
  mutate(scaledMeanValue=scale(meanValue),
         scaledValueDiff=scale(valueDiff),
         scaledTrialNum=scale(trialN))

contrasts(df.total.ddl$catChoiceCondition)<-contr.sdif
contrasts(df.total.rt.ddl$catChoiceCondition)<-contr.sdif
df.total.rt.ddl$scaledRT<-scale(log10(df.total.rt.ddl$firstRT))
df.total.rt.ddl$acc<-as.factor(df.total.rt.ddl$isBestFirst)
contrasts(df.total.rt.ddl$acc)<-contr.sum

df.total.rt.ddl$rr <- df.total.rt.ddl$firstValue/df.total.rt.ddl$firstRT

model.rr <- lmerTest::lmer(rr ~ catChoiceCondition * ( scaledMeanValue + scaledValueDiff) + scaledTrialNum + (1 + catChoiceCondition * ( scaledMeanValue + scaledValueDiff) + scaledTrialNum|participant),data=df.total.rt.ddl)

## boundary (singular) fit: see help('isSingular')

## Warning: Model failed to converge with 1 negative eigenvalue: -3.1e+01

model.RT <- lmerTest::lmer(firstRT ~ catChoiceCondition * scaledMeanValue + catChoiceCondition * scaledValueDiff + scaledTrialNum + (1 + catChoiceCondition * scaledMeanValue + catChoiceCondition * scaledValueDiff + scaledTrialNum|participant),data=df.total.rt.ddl)

## boundary (singular) fit: see help('isSingular')

## Warning: Model failed to converge with 3 negative eigenvalues: -3.6e-01
## -9.5e-01 -2.3e+03

model.acc <- glmer(isBestFirst ~ catChoiceCondition * scaledMeanValue +  catChoiceCondition * scaledValueDiff + scaledTrialNum + (1 + catChoiceCondition * scaledMeanValue +  catChoiceCondition * scaledValueDiff + scaledTrialNum|participant),data=df.total.rt.ddl,family = binomial)

## boundary (singular) fit: see help('isSingular')

model.acc.dummy <- lmer(isBestFirst ~ catChoiceCondition * scaledMeanValue +  catChoiceCondition * scaledValueDiff + scaledTrialNum + (1 + catChoiceCondition * scaledMeanValue +  catChoiceCondition * scaledValueDiff + scaledTrialNum|participant),data=df.total.rt.ddl)

## boundary (singular) fit: see help('isSingular')

# model.rr.ddl <- lmerTest::lmer(rr ~ catChoiceCondition * scaledMeanValue + catChoiceCondition * scaledValueDiff + scaledTrialNum + (1 + catChoiceCondition * scaledMeanValue + catChoiceCondition * scaledValueDiff + scaledTrialNum|participant),data=df.total.rt.ddl)

model.rating <- lmerTest::lmer(conflict ~ catChoiceCondition * poly(scaledMeanValue,2) + catChoiceCondition * scaledValueDiff + scaledTrialNum + (1 + catChoiceCondition * poly(scaledMeanValue,2) + scaledValueDiff|participant),data=df.total.ddl)

## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 0.00865799 (tol = 0.002, component 1)

## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: large eigenvalue ratio
##  - Rescale variables?

## Warning: Model failed to converge with 1 negative eigenvalue: -4.6e+00

library(kableExtra)

kbl(car::Anova(model.RT,type="III"),digits = 3) %>%
  kable_classic(full_width = F, html_font = "Cambria")

## Warning in printHypothesis(L, rhs, names(b)): one or more coefficients in the hypothesis include
##      arithmetic operators in their names;
##   the printed representation of the hypothesis will be omitted
## Warning in printHypothesis(L, rhs, names(b)): one or more coefficients in the hypothesis include
##      arithmetic operators in their names;
##   the printed representation of the hypothesis will be omitted
## Warning in printHypothesis(L, rhs, names(b)): one or more coefficients in the hypothesis include
##      arithmetic operators in their names;
##   the printed representation of the hypothesis will be omitted

	Chisq	Df	Pr(>Chisq)
(Intercept)	991.732	1	0
catChoiceCondition	106.936	1	0
scaledMeanValue	274.291	1	0
scaledValueDiff	83.856	1	0
scaledTrialNum	51.006	1	0
catChoiceCondition:scaledMeanValue	48.488	1	0
catChoiceCondition:scaledValueDiff	39.197	1	0

kbl(car::Anova(model.acc,type="III"),digits = 3) %>%
  kable_classic(full_width = F, html_font = "Cambria")

## Warning in printHypothesis(L, rhs, names(b)): one or more coefficients in the hypothesis include
##      arithmetic operators in their names;
##   the printed representation of the hypothesis will be omitted
## Warning in printHypothesis(L, rhs, names(b)): one or more coefficients in the hypothesis include
##      arithmetic operators in their names;
##   the printed representation of the hypothesis will be omitted
## Warning in printHypothesis(L, rhs, names(b)): one or more coefficients in the hypothesis include
##      arithmetic operators in their names;
##   the printed representation of the hypothesis will be omitted

	Chisq	Df	Pr(>Chisq)
(Intercept)	28.115	1	0.000
catChoiceCondition	9.336	1	0.002
scaledMeanValue	0.082	1	0.775
scaledValueDiff	287.903	1	0.000
scaledTrialNum	0.542	1	0.462
catChoiceCondition:scaledMeanValue	0.253	1	0.615
catChoiceCondition:scaledValueDiff	0.877	1	0.349

kbl(car::Anova(model.rating,type="III"),digits = 3) %>%
  kable_classic(full_width = F, html_font = "Cambria")

## Warning in printHypothesis(L, rhs, names(b)): one or more coefficients in the hypothesis include
##      arithmetic operators in their names;
##   the printed representation of the hypothesis will be omitted
## Warning in printHypothesis(L, rhs, names(b)): one or more coefficients in the hypothesis include
##      arithmetic operators in their names;
##   the printed representation of the hypothesis will be omitted
## Warning in printHypothesis(L, rhs, names(b)): one or more coefficients in the hypothesis include
##      arithmetic operators in their names;
##   the printed representation of the hypothesis will be omitted

	Chisq	Df	Pr(>Chisq)
(Intercept)	1876.556	1	0.000
catChoiceCondition	0.645	1	0.422
poly(scaledMeanValue, 2)	46.932	2	0.000
scaledValueDiff	15.930	1	0.000
scaledTrialNum	1.419	1	0.234
catChoiceCondition:poly(scaledMeanValue, 2)	0.826	2	0.662
catChoiceCondition:scaledValueDiff	5.341	1	0.021

model.RT.coeff <- lmerTest::lmer(firstRT ~ catChoiceCondition / scaledMeanValue + catChoiceCondition / scaledValueDiff + scaledTrialNum + 
                     (1 + catChoiceCondition / scaledMeanValue + catChoiceCondition / scaledValueDiff + scaledTrialNum|participant), 
                   data=df.total.rt.ddl)

## boundary (singular) fit: see help('isSingular')

## Warning: Model failed to converge with 1 negative eigenvalue: -2.5e+01

coeff.mat.RT <- coef(summary(model.RT.coeff))
coeff.mat.RT.ov <- data.frame(coeff.mat.RT[c('catChoiceCondition3:scaledMeanValue',
                                      'catChoiceCondition60:scaledMeanValue'),
                                    c('Estimate','Std. Error')])
coeff.mat.RT.ov$catChoiceCondition <- c('OR','XOR')
colnames(coeff.mat.RT.ov) <- c('beta_OV','se_OV','catChoiceCondition')
coeff.mat.RT.vd <- data.frame(coeff.mat.RT[c('catChoiceCondition3:scaledValueDiff',
                                      'catChoiceCondition60:scaledValueDiff')
                                    ,c('Estimate','Std. Error')])
coeff.mat.RT.vd$catChoiceCondition <- c('OR','XOR')
colnames(coeff.mat.RT.vd) <- c('beta_VD','se_VD','catChoiceCondition')

coeff.mat.RT <- inner_join(data.frame(coeff.mat.RT.ov),
                             data.frame(coeff.mat.RT.vd),by='catChoiceCondition') %>% mutate(study='Study DDL')
rownames(coeff.mat.RT) <- NULL

coeff.mat.RT <- rbind(coeff.mat.RT)

#coeff.mat.RT$catChoiceCondition <- rownames(coeff.mat.RT)

5.0.1 Extract coefficents in DDL study

model.acc.coeff <- glmer(isBestFirst ~ catChoiceCondition / scaledMeanValue + catChoiceCondition / scaledValueDiff + scaledTrialNum + 
                     (1 + catChoiceCondition / scaledMeanValue + catChoiceCondition / scaledValueDiff + scaledTrialNum|participant),
                     data=df.total.rt.ddl,family=binomial)

## Warning in (function (fn, par, lower = rep.int(-Inf, n), upper = rep.int(Inf, :
## failure to converge in 10000 evaluations

## Warning in optwrap(optimizer, devfun, start, rho$lower, control = control, :
## convergence code 4 from Nelder_Mead: failure to converge in 10000 evaluations

## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## unable to evaluate scaled gradient

## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge: degenerate Hessian with 1 negative eigenvalues

coeff.mat.Acc <- coef(summary(model.acc.coeff))
coeff.mat.Acc.ov <- data.frame(coeff.mat.Acc[c('catChoiceCondition3:scaledMeanValue',
                                      'catChoiceCondition60:scaledMeanValue'),
                                    c('Estimate','Std. Error')])
coeff.mat.Acc.ov$catChoiceCondition <- c('OR','XOR')
colnames(coeff.mat.Acc.ov) <- c('beta_OV','se_OV','catChoiceCondition')
coeff.mat.Acc.vd <- data.frame(coeff.mat.Acc[c('catChoiceCondition3:scaledValueDiff',
                                      'catChoiceCondition60:scaledValueDiff')
                                    ,c('Estimate','Std. Error')])
coeff.mat.Acc.vd$catChoiceCondition <- c('OR','XOR')
colnames(coeff.mat.Acc.vd) <- c('beta_VD','se_VD','catChoiceCondition')

coeff.mat.Acc <- inner_join(data.frame(coeff.mat.Acc.ov),
                             data.frame(coeff.mat.Acc.vd),by='catChoiceCondition') %>% mutate(study='Study DDL')
rownames(coeff.mat.Acc) <- NULL

coeff.mat.Acc <- rbind(coeff.mat.Acc)

coeff.mat.RT.total <- rbind(coeff.mat.RT,coeff.mat.RT.12) %>% mutate(color=c('DDL','NULL','OR','NULL'))


coeff.mat.Acc.total <- rbind(coeff.mat.Acc,coeff.mat.Acc.12) %>% mutate(color=c('DDL','NULL','OR','NULL'))

coeff.mat.RT.total$catChoiceCondition <- relevel(factor(coeff.mat.RT.total$catChoiceCondition),'XOR')
p.rt.mv.coeff.summary.14 <- ggplot(coeff.mat.RT.total %>% filter(study %in% c('Study 12','Study DDL')),aes(x = study,y=beta_OV,group=catChoiceCondition,color=color)) + geom_point(position = position_dodge(0.5),size=1) + geom_errorbar(position=position_dodge(0.5),aes(ymin=beta_OV-se_OV,ymax=beta_OV+se_OV,color=color),width=0.1) + theme_bw(12) + theme(panel.border = element_blank(), panel.grid.major = element_blank(), plot.title = element_text(hjust = 0.5,size=6),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",0.2),
        axis.ticks=element_line(colour='black',0.2)) + 
  theme(legend.justification=c(1,1),legend.position='none',text = element_text(size=6)) + ylab('Effect of OV') + xlab('') + scale_x_discrete(labels=c('Inclusivity','Urgency')) + scale_color_manual(values=c('#B02000','#0673C3',"#00B024"))  + scale_y_continuous(limits = c(-0.5,0.05),breaks=c(-0.5,0)) + geom_hline(yintercept = 0,linetype="dashed",size=0.2)

p.rt.mv.coeff.summary.14

coeff.mat.RT.total$catChoiceCondition <- relevel(factor(coeff.mat.RT.total$catChoiceCondition),'XOR')
p.rt.vd.coeff.summary.14 <- ggplot(coeff.mat.RT.total %>% filter(study %in% c('Study 12','Study DDL')),aes(x = study,y=beta_VD,group=catChoiceCondition,color=color)) + geom_point(position = position_dodge(0.5),size=1) + geom_errorbar(position=position_dodge(0.5),aes(ymin=beta_VD-se_VD,ymax=beta_VD+se_VD,color=color),width=0.1) + theme_bw(12) + theme(panel.border = element_blank(), panel.grid.major = element_blank(), plot.title = element_text(hjust = 0.5,size=6),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",0.2),
        axis.ticks=element_line(colour='black',0.2)) + 
  theme(legend.justification=c(1,1),legend.position='none',text = element_text(size=6)) + ylab('Effect of RV') + xlab('') + scale_x_discrete(labels=c('Inclusivity','Urgency')) + scale_color_manual(values=c('#B02000','#0673C3',"#00B024"))  + scale_y_continuous(limits = c(-0.5,0.05),breaks=c(-0.5,0)) + geom_hline(yintercept = 0,linetype="dashed",size=0.2)

p.rt.vd.coeff.summary.14

model.rating.coeff <- lmer(conflict ~ catChoiceCondition / poly(scaledMeanValue,2) + catChoiceCondition / scaledValueDiff + scaledTrialNum + 
                     (1 + catChoiceCondition / poly(scaledMeanValue,2) + catChoiceCondition / scaledValueDiff + scaledTrialNum|participant),
                     data=df.total.ddl)

## boundary (singular) fit: see help('isSingular')

model.rating.coeff.12 <- lmer(conflict ~ catChoiceCondition / poly(scaledMeanValue,2) + catChoiceCondition / scaledValueDiff + scaledTrialNum + 
                     (1 + catChoiceCondition / poly(scaledMeanValue,2) + catChoiceCondition / scaledValueDiff + scaledTrialNum|participant),
                     data=df.total.valid.12)

## boundary (singular) fit: see help('isSingular')

coeff.mat.rating <- coef(summary(model.rating.coeff))
coeff.mat.rating.ov <- data.frame(coeff.mat.rating[c('catChoiceCondition3:poly(scaledMeanValue, 2)1',
                                      'catChoiceCondition60:poly(scaledMeanValue, 2)1'),
                                    c('Estimate','Std. Error')])
coeff.mat.rating.ov$catChoiceCondition <- c('OR','XOR')
colnames(coeff.mat.rating.ov) <- c('beta_OV','se_OV','catChoiceCondition')
coeff.mat.rating.vd <- data.frame(coeff.mat.rating[c('catChoiceCondition3:scaledValueDiff',
                                      'catChoiceCondition60:scaledValueDiff')
                                    ,c('Estimate','Std. Error')])
coeff.mat.rating.vd$catChoiceCondition <- c('OR','XOR')
colnames(coeff.mat.rating.vd) <- c('beta_VD','se_VD','catChoiceCondition')

coeff.mat.rating <- inner_join(data.frame(coeff.mat.rating.ov),
                             data.frame(coeff.mat.rating.vd),by='catChoiceCondition') %>% mutate(study='Study DDL')
rownames(coeff.mat.rating) <- NULL

coeff.mat.rating <- rbind(coeff.mat.rating)

#coeff.mat.RT$catChoiceCondition <- rownames(coeff.mat.RT)

coeff.mat.rating.12 <- coef(summary(model.rating.coeff.12))
coeff.mat.rating.12.ov <- data.frame(coeff.mat.rating.12[c('catChoiceConditionOR:poly(scaledMeanValue, 2)1',
                                      'catChoiceConditionXOR:poly(scaledMeanValue, 2)1'),
                                    c('Estimate','Std. Error')])
coeff.mat.rating.12.ov$catChoiceCondition <- c('OR','XOR')
colnames(coeff.mat.rating.12.ov) <- c('beta_OV','se_OV','catChoiceCondition')
coeff.mat.rating.12.vd <- data.frame(coeff.mat.rating.12[c('catChoiceConditionOR:scaledValueDiff',
                                      'catChoiceConditionXOR:scaledValueDiff')
                                    ,c('Estimate','Std. Error')])
coeff.mat.rating.12.vd$catChoiceCondition <- c('OR','XOR')
colnames(coeff.mat.rating.12.vd) <- c('beta_VD','se_VD','catChoiceCondition')

coeff.mat.rating.12 <- inner_join(data.frame(coeff.mat.rating.12.ov),
                             data.frame(coeff.mat.rating.12.vd),by='catChoiceCondition') %>% mutate(study='Study 12')
rownames(coeff.mat.rating.12) <- NULL

coeff.mat.rating.12 <- rbind(coeff.mat.rating.12)

#coeff.mat.RT$catChoiceCondition <- rownames(coeff.mat.RT)

coeff.mat.rating.total <- rbind(coeff.mat.rating,coeff.mat.rating.12) %>% mutate(color=c('DDL','NULL','OR','NULL'))

coeff.mat.rating.total$catChoiceCondition <- relevel(factor(coeff.mat.rating.total$catChoiceCondition),'XOR')
p.cfl.mv.coeff.summary.14 <-ggplot(coeff.mat.rating.total %>% filter(study %in% c('Study 12','Study DDL')),aes(x = study,y=beta_OV,group=catChoiceCondition,color=color)) + geom_point(position = position_dodge(0.5),size=1) + geom_errorbar(position=position_dodge(0.5),aes(ymin=beta_OV-se_OV,ymax=beta_OV+se_OV,color=color),width=0.1) + theme_bw(12) + theme(panel.border = element_blank(), panel.grid.major = element_blank(), plot.title = element_text(hjust = 0.5,size=6),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",0.2),
        axis.ticks=element_line(colour='black',0.2)) + 
  theme(legend.justification=c(1,1),legend.position='none',text = element_text(size=6)) + ylab('Effect of OV\n(1st Order)') + xlab('') + scale_x_discrete(labels=c('Inclusivity','Urgency')) + scale_color_manual(values=c('#B02000','#0673C3',"#00B024")) + scale_y_continuous(limits = c(-10,40),breaks=c(0,40))+geom_hline(yintercept = 0,linetype="dashed",size=0.2)

p.cfl.mv.coeff.summary.14

coeff.mat.rating.total$catChoiceCondition <- relevel(factor(coeff.mat.rating.total$catChoiceCondition),'XOR')
p.cfl.vd.coeff.summary.14 <-ggplot(coeff.mat.rating.total %>% filter(study %in% c('Study 12','Study DDL')),aes(x = study,y=beta_VD,group=catChoiceCondition,color=color)) + geom_point(position = position_dodge(0.5),size=1) + geom_errorbar(position=position_dodge(0.5),aes(ymin=beta_VD-se_VD,ymax=beta_VD+se_VD,color=color),width=0.1) + theme_bw(12) + theme(panel.border = element_blank(), panel.grid.major = element_blank(), plot.title = element_text(hjust = 0.5,size=6),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",0.2),
        axis.ticks=element_line(colour='black',0.2)) + 
  theme(legend.justification=c(1,1),legend.position='none',text = element_text(size=6)) + ylab('Effect of RV') + xlab('') + scale_x_discrete(labels=c('Inclusivity','Urgency')) + scale_color_manual(values=c('#B02000','#0673C3',"#00B024")) + scale_y_continuous(limits = c(-0.15,0.025),breaks=c(-0.15,0))+geom_hline(yintercept = 0,linetype="dashed",size=0.2)

p.cfl.vd.coeff.summary.14

lay <- rbind(c(1,2),c(3,4))

plots <- list(p.rt.mv.coeff.summary.14,p.rt.vd.coeff.summary.14,
              p.cfl.mv.coeff.summary.14,p.cfl.vd.coeff.summary.14)

grobs <- list()
widths <- list()
heights <- list()

for (i in 1:length(plots)){
    grobs[[i]] <- ggplotGrob(plots[[i]])
    widths[[i]] <- grobs[[i]]$widths
    heights[[i]] <- grobs[[i]]$heights
    
}

maxwidth <- do.call(grid::unit.pmax, widths)
maxheight <- do.call(grid::unit.pmax,heights)

for (i in 1:length(grobs)){
     grobs[[i]]$heights <- as.list(maxheight)
     grobs[[i]]$widths <- as.list(maxwidth)
}

p<-grid.arrange(grobs = grobs, layout_matrix = lay,widths=unit(c(3.5,3.5), c("cm", "cm")),heights=unit(c(3.5,3.5),c('cm','cm')))

ggsave(filename = '../Figures/Figure8_V4.pdf',p,units = 'cm',width = 15,height = 15)

poly.mv <- poly(df.total.ddl$scaledMeanValue,2)
df.total.ddl$mvL <- poly.mv[,1]
df.total.ddl$mvQ <- poly.mv[,2]

model.rating.direct <- lmerTest::lmer(conflict ~ catChoiceCondition * (mvL + mvQ) + catChoiceCondition * scaledValueDiff + scaledTrialNum + (1 + catChoiceCondition * (mvL + mvQ) + catChoiceCondition * scaledValueDiff + scaledTrialNum|participant),data=df.total.ddl)

## boundary (singular) fit: see help('isSingular')

eff_mv.cfl.ddl <- Effect(c("scaledMeanValue","catChoiceCondition"),
                   model.rating,
                   xlevels=list(scaledMeanValue=seq(quantile(df.total.ddl$scaledMeanValue,0.025),
                                                    quantile(df.total.ddl$scaledMeanValue,0.975),0.1)))

## Warning in Analyze.model(focal.predictors, mod, xlevels, default.levels, : the
## predictors scaledValueDiff, scaledTrialNum, scaledMeanValue are one-column
## matrices that were converted to vectors

IA.mv.cfl.ddl <- as.data.frame(eff_mv.cfl.ddl)

IA.mv.cfl.ddl$catChoiceCondition <- relevel(IA.mv.cfl.ddl$catChoiceCondition,ref = '60')

p.eff.mv.cfl.ddl<-ggplot(data=IA.mv.cfl.ddl, aes(x=scaledMeanValue, y=fit,group=catChoiceCondition)) + 
  geom_line(size=0.5,aes(color=catChoiceCondition))+theme_bw(12) +
  geom_ribbon(data=IA.mv.cfl.ddl, aes(x=scaledMeanValue, max = upper, min = lower,fill=catChoiceCondition),alpha=0.3, inherit.aes = FALSE)+ 
  xlab("Overall Value\n(z-scored)") + ylab("Conflict") + 
  theme(panel.border = element_blank(), panel.grid.major = element_blank(), plot.title = element_text(hjust = 0.5,size=6),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),
        axis.ticks = element_line(colour = "black",size=0.2)) +
  theme(legend.justification=c(1,1),legend.position='none',text = element_text(size=6),strip.text.y = element_blank()) + 
  scale_fill_manual("",values=c('#0673C3','#B00024')) + 
  scale_color_manual("",values=c('#0673C3','#B00024')) + 
  coord_cartesian(ylim=c(1.5,3.5)) + scale_y_continuous(breaks = c(2,3))

p.eff.mv.cfl.ddl

eff_vd.cfl.ddl <- Effect(c("scaledValueDiff","catChoiceCondition"),
                   model.rating,
                   xlevels=list(scaledValueDiff=seq(quantile(df.total.ddl$scaledValueDiff,0.025),
                                                    quantile(df.total.ddl$scaledValueDiff,0.975),0.1)))

## Warning in Analyze.model(focal.predictors, mod, xlevels, default.levels, : the
## predictors scaledValueDiff, scaledTrialNum, scaledMeanValue are one-column
## matrices that were converted to vectors

IA.vd.cfl.ddl <- as.data.frame(eff_vd.cfl.ddl)

IA.vd.cfl.ddl$catChoiceCondition <- relevel(IA.vd.cfl.ddl$catChoiceCondition,ref = '60')

p.eff.vd.cfl.ddl<-ggplot(data=IA.vd.cfl.ddl, aes(x=scaledValueDiff, y=fit,group=catChoiceCondition)) + 
  geom_line(size=0.5,aes(color=catChoiceCondition))+theme_bw(12) +
  geom_ribbon(data=IA.vd.cfl.ddl, aes(x=scaledValueDiff, max = upper, min = lower,fill=catChoiceCondition),alpha=0.3, inherit.aes = FALSE)+ 
  xlab("Relative Value\n(z-scored)") + ylab("Conflict") + 
  theme(panel.border = element_blank(), panel.grid.major = element_blank(), plot.title = element_text(hjust = 0.5,size=6),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),
        axis.ticks = element_line(colour = "black",size=0.2)) +
  theme(legend.justification=c(1,1),legend.position='none',text = element_text(size=6),strip.text.y = element_blank()) + 
  scale_fill_manual("",values=c('#0673C3','#B00024')) + 
  scale_color_manual("",values=c('#0673C3','#B00024')) + 
  coord_cartesian(ylim=c(1.5,3.5)) + scale_y_continuous(breaks = c(2,3))

p.eff.vd.cfl.ddl

marginalConflictVDEffect <- function(model,x) {
  
  coeffs.mv.1 <- summary(model)$coeff[,'Estimate']
  
  eff <- coeffs.mv.1['catChoiceCondition3-60'] + 
    coeffs.mv.1['catChoiceCondition3-60:scaledValueDiff']*x
  
  cov.mat <- vcov(model)
  
  eff.ci <-  1.96 * sqrt(cov.mat[2,2] + x^2 * cov.mat[9,9] +
                                 2 * x * cov.mat[2,9])
  
  eff.df<-data.frame(x=x,eff=eff,ci=eff.ci)
  
  return(eff.df)
}

new.vd.1 <- seq(quantile(df.total.ddl$scaledValueDiff,0.025),
                quantile(df.total.ddl$scaledValueDiff,0.975),0.1)

eff.df.vd.ddl <- marginalConflictVDEffect(model.rating,new.vd.1) %>%
  dplyr::mutate(scaledValueDiff=x,
                catChoiceCondition='3 - 60',
                fit= eff,
                upper= eff+ci,
                lower= eff-ci,
                se=NA,
                study='Study 3')

p.eff.cc.int.ddl<-ggplot(data=eff.df.vd.ddl, aes(x=x, y=fit)) + 
  geom_line(size=0.5)+theme_bw(12) +
  geom_ribbon(data=eff.df.vd.ddl, aes(x=x, max = upper, min = lower),alpha=0.3, inherit.aes = FALSE)+ 
  xlab("Relative Value\n(z-scored)") + ylab('Effect of Urgency') +
  theme(panel.border = element_blank(), panel.grid.major = element_blank(), plot.title = element_text(hjust = 0.5,size=6),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),
        axis.ticks = element_line(colour = "black",size=0.2),
        strip.text.y = element_blank()) +
  theme(legend.justification=c(1,1),legend.position='none',text = element_text(size=6)) + geom_hline(yintercept=0,color='#555555',size=0.2) + 
  scale_fill_manual("",values=c("#005555","#550055")) + scale_color_manual("",values=c("#005555","#550055")) + # ggtitle('Exclusive - Non-Exclusive')#  +
  coord_cartesian(ylim=c(-.15,0.5)) + scale_y_continuous(breaks = c(0,0.5))

p.eff.cc.int.ddl

coeff.rt <- t(fixef(model.RT)['catChoiceCondition3-60'])
df.ci <- confint(model.RT,method="Wald")
df.ci <- df.ci[!is.na(df.ci[,1]),]
ci.rt <- df.ci['catChoiceCondition3-60',]
estimate.rt <- cbind(coeff.rt,t(ci.rt))
colnames(estimate.rt)<-c('coeff','lower','upper')

coeff.acc <- t(fixef(model.acc.dummy)['catChoiceCondition3-60'])
df.ci <- confint(model.acc.dummy,method="Wald")
df.ci <- df.ci[!is.na(df.ci[,1]),]
ci.acc <- df.ci['catChoiceCondition3-60',]
estimate.acc <- cbind(coeff.acc,t(ci.acc))
colnames(estimate.acc)<-c('coeff','lower','upper')

coeff.rr <- t(fixef(model.rr)['catChoiceCondition3-60'])
df.ci <- confint(model.rr,method="Wald")
df.ci <- df.ci[!is.na(df.ci[,1]),]
ci.rr <- df.ci['catChoiceCondition3-60',]
estimate.rr <- cbind(coeff.rr,t(ci.rr))
colnames(estimate.rr)<-c('coeff','lower','upper')

coeff.conf <- t(fixef(model.rating)['catChoiceCondition3-60'])
df.ci <- confint(model.rating,method="Wald")
df.ci <- df.ci[!is.na(df.ci[,1]),]
ci.conf <- df.ci['catChoiceCondition3-60',]
estimate.conf <- cbind(coeff.conf,t(ci.conf))
colnames(estimate.conf)<-c('coeff','lower','upper')

estimate.all <- data.frame(rbind(estimate.rt,estimate.acc,estimate.rr,estimate.conf))
estimate.all$var <- c('RT','Acc','RR','Conflict')

p.diff.acc.ddl <- ggplot(estimate.all %>% filter(var %in% c('Acc')), aes(x=var, y=coeff))  + geom_hline(yintercept=0,color='#555555',size=0.2) + 
  geom_point(stat="identity", position=position_dodge(0.6),size=0.5) +
  geom_errorbar(aes(ymin=lower, ymax=upper), width=0.1,size=0.4,
                 position=position_dodge(.6))+labs(x="", y = "Effect of Urgency")+theme_bw(12) + 
  theme(panel.border = element_blank(),panel.grid.major = element_blank(),
        axis.title.x = element_text(margin = margin(t = 0, r = 0, b = 0, l = 0)),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),
        axis.ticks = element_line(colour = "black",size=0.2),
        text=element_text(size=6),legend.position="none") +
  scale_x_discrete(labels=c("Acc"='P(Best First)')) + scale_y_continuous(limits = c(-0.1,0.01),breaks = c(-0.1,0))

p.diff.acc.ddl

p.diff.rt.ddl <- ggplot(estimate.all %>% filter(var %in% c('RT')), aes(x=var, y=coeff))  + geom_hline(yintercept=0,color='#555555',size=0.2) + 
  geom_point(stat="identity", position=position_dodge(0.6),size=0.5) +
  geom_errorbar(aes(ymin=lower, ymax=upper), width=0.1,size=0.4,
                 position=position_dodge(.6))+labs(x="", y = "Effect of Urgency\n(sec)")+theme_bw(12) + 
  theme(panel.border = element_blank(),panel.grid.major = element_blank(),
        axis.title.x = element_text(margin = margin(t = 0, r = 0, b = 0, l = 0)),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),
        axis.ticks = element_line(colour = "black",size=0.2),
        text=element_text(size=6),legend.position="none") +
  scale_x_discrete(labels=c("RT"='RT')) + scale_y_continuous(limits = c(-2,0.2),breaks = c(-2,0))

p.diff.rt.ddl

p.diff.rr.ddl <- ggplot(estimate.all %>% filter(var %in% c('RR')), aes(x=var, y=coeff))  + geom_hline(yintercept=0,color='#555555',szie=0.2) + 
  geom_point(stat="identity", position=position_dodge(0.6),size=0.5) +
  geom_errorbar(aes(ymin=lower, ymax=upper), width=0.1,size=0.4,
                 position=position_dodge(.6))+labs(x="", y = "Effect of Urgency\n(Unit Value/sec)")+theme_bw(12) + 
  theme(panel.border = element_blank(),panel.grid.major = element_blank(),
        axis.title.x = element_text(margin = margin(t = 0, r = 0, b = 0, l = 0)),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),
        axis.ticks = element_line(colour = "black",size=0.2),
        text=element_text(size=6),legend.position="none") +
  scale_x_discrete(labels=c("RR"='Reward Rate')) + scale_y_continuous(limits = c(-0.2,2),breaks = c(0,2))

## Warning in geom_hline(yintercept = 0, color = "#555555", szie = 0.2): Ignoring
## unknown parameters: `szie`

p.diff.rr.ddl

p.diff.conflict.ddl <- ggplot(estimate.all %>% filter(var %in% c('Conflict')), aes(x=var, y=coeff))  + geom_hline(yintercept=0,color='#555555') + 
  geom_point(stat="identity", position=position_dodge(0.6),size=0.5) +
  geom_errorbar(aes(ymin=lower, ymax=upper), width=0.1,size=0.4,
                 position=position_dodge(.6))+labs(x="", y = "Effect of Urgency")+theme_bw(12) + 
  theme(panel.border = element_blank(),panel.grid.major = element_blank(),
        axis.title.x = element_text(margin = margin(t = 0, r = 0, b = 0, l = 0)),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),
        axis.ticks = element_line(colour = "black",size=0.2),
        text=element_text(size=6),legend.position="none") +
  scale_x_discrete(labels=c("Conflict"='Conflict')) + scale_y_continuous(limits = c(-0.2,0.2),breaks = c(-0.2,0,0.2))
p.diff.conflict.ddl

eff_mv.RT.ddl <- Effect(c("scaledMeanValue","catChoiceCondition"),
                   model.RT,
                   xlevels=list(scaledMeanValue=seq(quantile(df.total.rt.ddl$scaledMeanValue,0.025),
                                                    quantile(df.total.rt.ddl$scaledMeanValue,0.975),0.1)))

## Warning in Analyze.model(focal.predictors, mod, xlevels, default.levels, : the
## predictors scaledMeanValue, scaledValueDiff, scaledTrialNum are one-column
## matrices that were converted to vectors

IA.mv.RT.ddl <- as.data.frame(eff_mv.RT.ddl) %>% dplyr::mutate(study='Study 3')

p.eff.mv.rt.ddl<-ggplot(data=IA.mv.RT.ddl, aes(x=scaledMeanValue, y=fit, group=catChoiceCondition)) +
  geom_line(size=0.5,aes(linetype=study,color=catChoiceCondition))+theme_bw(12) +
  geom_ribbon(data=IA.mv.RT.ddl, aes(x=scaledMeanValue, max = upper, min = lower,fill=catChoiceCondition),alpha=0.3, inherit.aes = FALSE)+ 
  xlab("Overall Value\n(z-scored)") + ylab("RT (sec)") + 
  theme(panel.border = element_blank(), panel.grid.major = element_blank(),
        axis.title.x = element_text(margin = margin(t = 0, r = 0, b = 0, l = 0)),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),
        axis.ticks = element_line(colour = "black",size=0.2)) +
  theme(legend.justification=c(1,1),legend.position='none',text = element_text(size=6)) + 
  scale_fill_manual("",values=c('#0673C3','#B00024')) + 
  scale_color_manual("",values=c('#0673C3','#B00024')) + 
  coord_cartesian(ylim=c(1,4)) + scale_y_continuous(breaks = c(1,4))

p.eff.mv.rt.ddl

eff_vd.RT.ddl <- Effect(c("scaledValueDiff","catChoiceCondition"),
                   model.RT,
                   xlevels=list(scaledValueDiff=seq(quantile(df.total.rt.ddl$scaledValueDiff,0.025),
                                                    quantile(df.total.rt.ddl$scaledValueDiff,0.975),0.1)))

## Warning in Analyze.model(focal.predictors, mod, xlevels, default.levels, : the
## predictors scaledMeanValue, scaledValueDiff, scaledTrialNum are one-column
## matrices that were converted to vectors

IA.vd.RT.ddl <- as.data.frame(eff_vd.RT.ddl) %>% dplyr::mutate(study='Study 3')

p.eff.vd.rt.ddl <-ggplot(data=IA.vd.RT.ddl, aes(x=scaledValueDiff, y=fit, group=catChoiceCondition)) +
  geom_line(size=0.5,aes(linetype=study,color=catChoiceCondition))+theme_bw(12) +
  geom_ribbon(data=IA.vd.RT.ddl, aes(x=scaledValueDiff, max = upper, min = lower,fill=catChoiceCondition),alpha=0.3, inherit.aes = FALSE)+ 
  xlab("Relative Value\n(z-scored)") + ylab("RT (sec)") + 
  theme(panel.border = element_blank(), panel.grid.major = element_blank(),
        axis.title.x = element_text(margin = margin(t = 0, r = 0, b = 0, l = 0)),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),
        axis.ticks = element_line(colour = "black",size=0.2)) +
  theme(legend.justification=c(1,1),legend.position='none',text = element_text(size=6)) + 
  scale_fill_manual("",values=c('#0673C3','#B00024')) + 
  scale_color_manual("",values=c('#0673C3','#B00024')) + 
  coord_cartesian(ylim=c(1,4)) + scale_y_continuous(breaks = c(1,4))

p.eff.vd.rt.ddl

eff_mv.acc.ddl <- Effect(c("scaledMeanValue","catChoiceCondition"),
                   model.acc,
                   xlevels=list(scaledMeanValue=seq(quantile(df.total.rt.ddl$scaledMeanValue,0.025),
                                                    quantile(df.total.rt.ddl$scaledMeanValue,0.972),0.1)))

## Warning in Analyze.model(focal.predictors, mod, xlevels, default.levels, : the
## predictors scaledMeanValue, scaledValueDiff, scaledTrialNum are one-column
## matrices that were converted to vectors

IA.mv.acc.ddl <- as.data.frame(eff_mv.acc.ddl) %>% dplyr::mutate(study='Study 3')

p.eff.mv.acc.ddl <-ggplot(data=IA.mv.acc.ddl, aes(x=scaledMeanValue, y=fit, group=catChoiceCondition)) +
  geom_line(size=0.5,aes(linetype=study,color=catChoiceCondition))+theme_bw(12) +
  geom_ribbon(data=IA.mv.acc.ddl, aes(x=scaledMeanValue, max = upper, min = lower,fill=catChoiceCondition),alpha=0.3, inherit.aes = FALSE)+ 
  xlab("Overall value\n(z-scored)") + ylab("P(Best First)") + 
  theme(panel.border = element_blank(), panel.grid.major = element_blank(),
        axis.title.x = element_text(margin = margin(t = 0, r = 0, b = 0, l = 0)),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),
        axis.ticks = element_line(colour = "black",size=0.2)) +
  theme(legend.justification=c(1,1),legend.position='none',text = element_text(size=6)) + 
  scale_fill_manual("",values=c('#0673C3','#B00024')) + 
  scale_color_manual("",values=c('#0673C3','#B00024')) + 
  coord_cartesian(ylim=c(0.1,0.9)) + scale_y_continuous(breaks = c(0.1,0.9),labels=function(x) sprintf("%.1f", x))

p.eff.mv.acc.ddl

#ggsave('Study12_RT.pdf')

eff_vd.acc.ddl <- Effect(c("scaledValueDiff","catChoiceCondition"),
                   model.acc,
                   xlevels=list(scaledValueDiff=seq(quantile(df.total.rt.ddl$scaledValueDiff,0.025),
                                                    quantile(df.total.rt.ddl$scaledValueDiff,0.975),0.1)))

## Warning in Analyze.model(focal.predictors, mod, xlevels, default.levels, : the
## predictors scaledMeanValue, scaledValueDiff, scaledTrialNum are one-column
## matrices that were converted to vectors

IA.vd.acc.ddl <- as.data.frame(eff_vd.acc.ddl) %>% dplyr::mutate(study='Study 3')

p.eff.vd.acc.ddl<-ggplot(data=IA.vd.acc.ddl, aes(x=scaledValueDiff, y=fit, group=catChoiceCondition)) +
  geom_line(size=0.5,aes(linetype=study,color=catChoiceCondition))+theme_bw(12) +
  geom_ribbon(data=IA.vd.acc.ddl, aes(x=scaledValueDiff, max = upper, min = lower,fill=catChoiceCondition),alpha=0.3, inherit.aes = FALSE)+ 
  xlab("Relative Value\n(z-scored)") + ylab("P(Best First)") + 
  theme(panel.border = element_blank(), panel.grid.major = element_blank(),
        axis.title.x = element_text(margin = margin(t = 0, r = 0, b = 0, l = 0)),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),
        axis.ticks = element_line(colour = "black",size=0.2)) +
  theme(legend.justification=c(1,1),legend.position='none',text = element_text(size=6)) + 
  scale_fill_manual("",values=c('#0673C3','#B00024')) + 
  scale_color_manual("",values=c('#0673C3','#B00024')) + 
  coord_cartesian(ylim=c(0.1,0.9)) + scale_y_continuous(breaks = c(0.1,0.9),labels=function(x) sprintf("%.1f", x))

p.eff.vd.acc.ddl

#ggsave('Study12_RT.pdf')

lay <- rbind(c(1, 4, 4, 4, 7),
             c(2, 2, NA,3, 3),
             c(5, 5, NA,6, 6))

plots <- list(p.diff.rt.ddl,p.eff.mv.rt.ddl,p.eff.vd.rt.ddl,
              p.diff.acc.ddl,p.eff.mv.acc.ddl,p.eff.vd.acc.ddl,p.diff.rr.ddl)
grobs <- list()
widths <- list()
heights <- list()

for (i in 1:length(plots)){
    grobs[[i]] <- ggplotGrob(plots[[i]])
    widths[[i]] <- grobs[[i]]$widths
    heights[[i]] <- grobs[[i]]$heights
}

maxwidth <- do.call(grid::unit.pmax, widths)
maxheight <- do.call(grid::unit.pmax,heights)

for (i in c(2,3,5,6)){
     grobs[[i]]$widths <- as.list(maxwidth)
}

for (i in 1:length(grobs)){
     grobs[[i]]$heights <- as.list(maxheight)
}

widths <- list()

for (i in c(1,4,7)){
    widths[[i]] <- grobs[[i]]$widths
}

maxwidth <- do.call(grid::unit.pmax,widths)

for (i in c(1,4,7)){
     grobs[[i]]$widths <- as.list(maxwidth)
}

p<-grid.arrange(grobs = grobs, layout_matrix = lay,widths=unit(c(2.1,0.9,0.2,0.9,2.1), c("cm", "cm")),heights=unit(c(3,3,3),c('cm','cm')))

ggsave(filename = '../Figures/FigureS5_V2.pdf',p,units = 'cm',width = 10,height = 15)

lay <- rbind(c(1,NA,2,NA,3,NA,4))

plots <- list(p.diff.conflict.ddl,p.eff.mv.cfl.ddl,p.eff.vd.cfl.ddl,p.eff.cc.int.ddl)
grobs <- list()
widths <- list()
heights <- list()

for (i in 1:length(plots)){
    grobs[[i]] <- ggplotGrob(plots[[i]])
    widths[[i]] <- grobs[[i]]$widths
    heights[[i]] <- grobs[[i]]$heights
}

maxwidth <- do.call(grid::unit.pmax, widths)
maxheight <- do.call(grid::unit.pmax, heights)

for (i in 1:length(grobs)){
  grobs[[i]]$widths <- as.list(maxwidth)
  grobs[[i]]$heights <- as.list(maxheight)
}

p<-grid.arrange(grobs = grobs, layout_matrix = lay,widths=unit(c(2.1,0.1,2.7,0.1,2.7,0.1,2.7), c("cm", "cm")),heights=unit(c(3),c('cm','cm')))

ggsave(filename = '../Figures/FigureS6_V2.pdf',p,units = 'cm',width = 25,height = 12)

df.orxorg <- read.csv('../Data/Study5/Study5a/Study5a_1.csv')
df.orxorg.rating <- read.csv('../Data/Study5/Study5a/Study5a_2.csv')

# df.orxorg.rt <- read.csv('Study5a/resp1.csv')

df.orxori <- read.csv('../Data/Study5/Study5b/Study5b_1.csv')
df.orxorg.rating <- read.csv('../Data/Study5/Study5b/Study5b_2.csv')

# df.orxori.rt <- read.csv('Study5b/resp2.csv')

df.orxorgi <- rbind(df.orxorg %>% select(participant,firstRT,isBestFirst,meanValue,valueDiff,choiceCondition,trialNGlobal,conflict),
                    df.orxori %>% select(participant,firstRT,isBestFirst,meanValue,valueDiff,choiceCondition,trialNGlobal,conflict)) %>%
  mutate(scaledMeanValue=scale(meanValue),
         scaledValueDiff=scale(valueDiff),
         scaledTrialNum=scale(trialNGlobal),
         catChoiceCondition=relevel(factor(choiceCondition,labels = c('OR','XOR')),ref = 'XOR'))

contrasts(df.orxorgi$catChoiceCondition) <- MASS::contr.sdif

df.orxorgi.rt <- rbind(df.orxorg %>% filter(firstRT>0.1) %>% select(participant,firstRT,isBestFirst,meanValue,valueDiff,choiceCondition,trialNGlobal,conflict),
                       df.orxori %>% filter(firstRT>0.1) %>% select(participant,firstRT,isBestFirst,meanValue,valueDiff,choiceCondition,trialNGlobal,conflict)) %>%
  mutate(scaledMeanValue=scale(meanValue),
         scaledValueDiff=scale(valueDiff),
         scaledTrialNum=scale(trialNGlobal),
         catChoiceCondition=relevel(factor(choiceCondition,labels = c('OR','XOR')),ref = 'XOR'))

contrasts(df.orxorgi.rt$catChoiceCondition) <- MASS::contr.sdif

model.logRT.gi <- lmer(log10(firstRT) ~ catChoiceCondition * (scaledMeanValue + scaledValueDiff) + scaledTrialNum + (1 + catChoiceCondition * (scaledMeanValue + scaledValueDiff) + scaledTrialNum|participant),data=df.orxorgi.rt)

## boundary (singular) fit: see help('isSingular')

model.acc.gi <- glmer(isBestFirst ~ catChoiceCondition * (scaledMeanValue + scaledValueDiff) + scaledTrialNum + (1 + catChoiceCondition * (scaledMeanValue + scaledValueDiff) + scaledTrialNum|participant),data=df.orxorgi.rt,family = binomial())

## Warning in (function (fn, par, lower = rep.int(-Inf, n), upper = rep.int(Inf, :
## failure to converge in 10000 evaluations

## Warning in optwrap(optimizer, devfun, start, rho$lower, control = control, :
## convergence code 4 from Nelder_Mead: failure to converge in 10000 evaluations

## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 0.0118834 (tol = 0.002, component 1)

model.conflict.gi <- lmer(conflict ~ catChoiceCondition * (poly(scaledMeanValue,2) + scaledValueDiff) + scaledTrialNum + (1 + catChoiceCondition * (poly(scaledMeanValue,2) + scaledValueDiff) + scaledTrialNum|participant),data=df.orxorgi)

## boundary (singular) fit: see help('isSingular')

df.orxori.total <- df.orxori %>% select(participant,firstRT,isBestFirst,meanValue,valueDiff,choiceCondition,trialNGlobal,conflict) %>%
  mutate(scaledMeanValue=scale(meanValue),
         scaledValueDiff=scale(valueDiff),
         scaledTrialNum=scale(trialNGlobal),
         catChoiceCondition=relevel(factor(choiceCondition,labels = c('OR','XOR')),ref = 'XOR'))

contrasts(df.orxori.total$catChoiceCondition) <- MASS::contr.sdif

df.orxori.rt <- df.orxori.total %>% filter(firstRT>0.1) %>% select(participant,firstRT,isBestFirst,meanValue,valueDiff,choiceCondition,trialNGlobal,conflict) %>%
  mutate(scaledMeanValue=scale(meanValue),
         scaledValueDiff=scale(valueDiff),
         scaledTrialNum=scale(trialNGlobal),
         catChoiceCondition=relevel(factor(choiceCondition,labels = c('OR','XOR')),ref = 'XOR'))

contrasts(df.orxori.rt$catChoiceCondition) <- MASS::contr.sdif

model.logRT.i <- lmer(log10(firstRT) ~ catChoiceCondition * (scaledMeanValue + scaledValueDiff) + scaledTrialNum + (1 + catChoiceCondition * (scaledMeanValue + scaledValueDiff) + scaledTrialNum|participant),data=df.orxori.rt)

## boundary (singular) fit: see help('isSingular')

model.acc.i <- glmer(isBestFirst ~ catChoiceCondition * (scaledMeanValue + scaledValueDiff) + scaledTrialNum + (1 + catChoiceCondition * (scaledMeanValue + scaledValueDiff) + scaledTrialNum|participant),data=df.orxori.rt,family = binomial())

## Warning in (function (fn, par, lower = rep.int(-Inf, n), upper = rep.int(Inf, :
## failure to converge in 10000 evaluations

## Warning in optwrap(optimizer, devfun, start, rho$lower, control = control, :
## convergence code 4 from Nelder_Mead: failure to converge in 10000 evaluations

## boundary (singular) fit: see help('isSingular')

model.conflict.i <- lmer(conflict ~ catChoiceCondition * (poly(scaledMeanValue,2) + scaledValueDiff) + scaledTrialNum + (1 + catChoiceCondition * (poly(scaledMeanValue,2) + scaledValueDiff) + scaledTrialNum|participant),data=df.orxori.total)

## boundary (singular) fit: see help('isSingular')

new.mv <- seq(quantile(df.orxorgi$scaledMeanValue,0.025),
              quantile(df.orxorgi$scaledMeanValue,0.975),0.1)

eff.df.mv.gi <- marginalConflictMVEffect(model.conflict.gi,df.orxorgi$scaledMeanValue,new.mv) %>%
  dplyr::mutate(scaledMeanValue=x,
                catChoiceCondition='XOR - OR',
                fit= eff,
                upper= eff+ci,
                lower= eff-ci,
                se=NA,
                study='Study 3')

p.eff.cc.int.gi<-ggplot(data=eff.df.mv.gi, aes(x=x, y=fit)) + 
  geom_line(size=0.5)+theme_bw(12) +
  geom_ribbon(data=eff.df.mv.gi, aes(x=x, max = upper, min = lower),alpha=0.3, inherit.aes = FALSE)+ 
  xlab("Overall value\n(z-scored)") + ylab('Effect of Inclusivity') +
  theme(panel.border = element_blank(), panel.grid.major = element_blank(), plot.title = element_text(hjust = 0.5,size=6),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),
        axis.ticks = element_line(colour = "black",size=0.2),
        strip.text.y = element_blank()) +
  theme(legend.justification=c(1,1),legend.position='none',text = element_text(size=6)) + geom_hline(yintercept=0,color='#555555',size=0.2) + 
  scale_fill_manual("",values=c("#005555","#550055")) + scale_color_manual("",values=c("#005555","#550055")) + # ggtitle('Exclusive - Non-Exclusive') +
  coord_cartesian(ylim=c(-1,0.3)) + scale_y_continuous(breaks = c(-1,0))

p.eff.cc.int.gi

ggsave(filename = '../Figures/FigureS1B.pdf',p.eff.cc.int.gi,units = 'cm',width = 3,height = 3)

new.mv <- seq(quantile(df.orxori.total$scaledMeanValue,0.025),
              quantile(df.orxori.total$scaledMeanValue,0.975),0.1)

eff.df.mv.i <- marginalConflictMVEffect(model.conflict.i,df.orxori.total$scaledMeanValue,new.mv) %>%
  dplyr::mutate(scaledMeanValue=x,
                catChoiceCondition='XOR - OR',
                fit= eff,
                upper= eff+ci,
                lower= eff-ci,
                se=NA,
                study='Study 3')

p.eff.cc.int.i<-ggplot(data=eff.df.mv.i, aes(x=x, y=fit)) + 
  geom_line(size=0.5)+theme_bw(12) +
  geom_ribbon(data=eff.df.mv.i, aes(x=x, max = upper, min = lower),alpha=0.3, inherit.aes = FALSE)+ 
  xlab("Overall value\n(z-scored)") + ylab('Effect of Inclusivity') +
  theme(panel.border = element_blank(), panel.grid.major = element_blank(), plot.title = element_text(hjust = 0.5,size=6),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),
        axis.ticks = element_line(colour = "black",size=0.2),
        strip.text.y = element_blank()) +
  theme(legend.justification=c(1,1),legend.position='none',text = element_text(size=6)) + geom_hline(yintercept=0,color='#555555',size=0.2) + 
  scale_fill_manual("",values=c("#005555","#550055")) + scale_color_manual("",values=c("#005555","#550055")) + # ggtitle('Exclusive - Non-Exclusive') +
  coord_cartesian(ylim=c(-1,0.3)) + scale_y_continuous(breaks = c(-1,0))

p.eff.cc.int.i

ggsave(filename = '../Figures/FigureS2B.pdf',p.eff.cc.int.i,units = 'cm',width = 3,height = 3)

coeff.rt.ns <- fixef(model.logRT.gi)[c('catChoiceConditionOR-XOR','catChoiceConditionOR-XOR:scaledMeanValue','catChoiceConditionOR-XOR:scaledValueDiff')]
df.ci <- confint(model.logRT.gi,method="Wald")
df.ci <- df.ci[!is.na(df.ci[,1]),]
ci.rt <- df.ci[c('catChoiceConditionOR-XOR','catChoiceConditionOR-XOR:scaledMeanValue','catChoiceConditionOR-XOR:scaledValueDiff'),]
estimate.rt.gi <- t(rbind(coeff.rt.ns,t(ci.rt)))
colnames(estimate.rt.gi)<-c('coeff','lower','upper')
rownames(estimate.rt.gi) <- NULL
estimate.rt.gi <- data.frame(estimate.rt.gi)
estimate.rt.gi$params <- c('Incl - Excl','(Incl - Excl) X OV','(Incl - Excl) X RV')
estimate.rt.gi$dv <- 'RT'

p.summary.gi.rt <- ggplot(estimate.rt.gi,aes(x=params,y=coeff)) + geom_hline(yintercept=0,color='#AAAAAA',size=0.2) + geom_point(position = position_dodge(0.6),size=0.5) + geom_errorbar(position = position_dodge(0.6),aes(ymin=lower,ymax=upper),width=0.2) + coord_flip() + theme_bw(12) + 
  theme(panel.border = element_blank(),panel.grid.major = element_blank(),
        axis.title.x = element_text(margin = margin(t = 0, r = 0, b = 0, l = 0)),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),
        axis.ticks = element_line(colour = "black",size=0.2),
        text=element_text(size=6),legend.position="none") + scale_y_continuous(limits = c(-0.04,0.04),breaks = c(-0.04,0,0.04)) + xlab('') + ylab('') + scale_x_discrete(labels=c('Incl - Excl'='On intercept','(Incl - Excl) X OV'='On overall value effect','(Incl - Excl) X RV'='On relative value effect'))
p.summary.gi.rt

ggsave(filename = '../Figures/FigureS1A.pdf',p.summary.gi.rt,units = 'cm',width = 4.8,height = 3)

coeff.rt.ns <- fixef(model.logRT.i)[c('catChoiceConditionOR-XOR','catChoiceConditionOR-XOR:scaledMeanValue','catChoiceConditionOR-XOR:scaledValueDiff')]
df.ci <- confint(model.logRT.i,method="Wald")
df.ci <- df.ci[!is.na(df.ci[,1]),]
ci.rt <- df.ci[c('catChoiceConditionOR-XOR','catChoiceConditionOR-XOR:scaledMeanValue','catChoiceConditionOR-XOR:scaledValueDiff'),]
estimate.rt.i <- t(rbind(coeff.rt.ns,t(ci.rt)))
colnames(estimate.rt.i)<-c('coeff','lower','upper')
rownames(estimate.rt.i) <- NULL
estimate.rt.i <- data.frame(estimate.rt.i)
estimate.rt.i$params <- c('Incl - Excl','(Incl - Excl) X OV','(Incl - Excl) X RV')
estimate.rt.i$dv <- 'RT'

p.summary.i.rt <- ggplot(estimate.rt.i,aes(x=params,y=coeff)) + geom_hline(yintercept=0,color='#AAAAAA',size=0.2) + geom_point(position = position_dodge(0.6),size=0.5) + geom_errorbar(position = position_dodge(0.6),aes(ymin=lower,ymax=upper),width=0.2) + coord_flip() + theme_bw(12) + 
  theme(panel.border = element_blank(),panel.grid.major = element_blank(),
        axis.title.x = element_text(margin = margin(t = 0, r = 0, b = 0, l = 0)),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),
        axis.ticks = element_line(colour = "black",size=0.2),
        text=element_text(size=6),legend.position="none") + scale_y_continuous(limits = c(-0.04,0.04),breaks = c(-0.04,0,0.04)) + xlab('') + ylab('') + scale_x_discrete(labels=c('Incl - Excl'='On intercept','(Incl - Excl) X OV'='On overall value effect','(Incl - Excl) X RV'='On relative value effect'))
p.summary.i.rt

ggsave(filename = '../Figures/FigureS2A.pdf',p.summary.i.rt,units = 'cm',width = 4.8,height = 3)

library(kableExtra)
kbl(car::Anova(model.logRT.gi,type="3"),digits = 3) %>%
  kable_classic(full_width = F, html_font = "Cambria")

## Warning in printHypothesis(L, rhs, names(b)): one or more coefficients in the hypothesis include
##      arithmetic operators in their names;
##   the printed representation of the hypothesis will be omitted
## Warning in printHypothesis(L, rhs, names(b)): one or more coefficients in the hypothesis include
##      arithmetic operators in their names;
##   the printed representation of the hypothesis will be omitted
## Warning in printHypothesis(L, rhs, names(b)): one or more coefficients in the hypothesis include
##      arithmetic operators in their names;
##   the printed representation of the hypothesis will be omitted

	Chisq	Df	Pr(>Chisq)
(Intercept)	960.803	1	0.000
catChoiceCondition	21.239	1	0.000
scaledMeanValue	109.712	1	0.000
scaledValueDiff	304.755	1	0.000
scaledTrialNum	167.979	1	0.000
catChoiceCondition:scaledMeanValue	13.097	1	0.000
catChoiceCondition:scaledValueDiff	0.639	1	0.424

kbl(car::Anova(model.acc.gi,type="3"),digits = 3) %>%
  kable_classic(full_width = F, html_font = "Cambria")

## Warning in printHypothesis(L, rhs, names(b)): one or more coefficients in the hypothesis include
##      arithmetic operators in their names;
##   the printed representation of the hypothesis will be omitted
## Warning in printHypothesis(L, rhs, names(b)): one or more coefficients in the hypothesis include
##      arithmetic operators in their names;
##   the printed representation of the hypothesis will be omitted
## Warning in printHypothesis(L, rhs, names(b)): one or more coefficients in the hypothesis include
##      arithmetic operators in their names;
##   the printed representation of the hypothesis will be omitted

	Chisq	Df	Pr(>Chisq)
(Intercept)	36.082	1	0.000
catChoiceCondition	1.343	1	0.247
scaledMeanValue	3.413	1	0.065
scaledValueDiff	471.864	1	0.000
scaledTrialNum	1.768	1	0.184
catChoiceCondition:scaledMeanValue	0.251	1	0.617
catChoiceCondition:scaledValueDiff	1.690	1	0.194

kbl(car::Anova(model.conflict.gi,type="3"),digits = 3) %>%
  kable_classic(full_width = F, html_font = "Cambria")

## Warning in printHypothesis(L, rhs, names(b)): one or more coefficients in the hypothesis include
##      arithmetic operators in their names;
##   the printed representation of the hypothesis will be omitted
## Warning in printHypothesis(L, rhs, names(b)): one or more coefficients in the hypothesis include
##      arithmetic operators in their names;
##   the printed representation of the hypothesis will be omitted
## Warning in printHypothesis(L, rhs, names(b)): one or more coefficients in the hypothesis include
##      arithmetic operators in their names;
##   the printed representation of the hypothesis will be omitted

	Chisq	Df	Pr(>Chisq)
(Intercept)	1295.542	1	0.000
catChoiceCondition	12.575	1	0.000
poly(scaledMeanValue, 2)	63.126	2	0.000
scaledValueDiff	16.882	1	0.000
scaledTrialNum	0.257	1	0.612
catChoiceCondition:poly(scaledMeanValue, 2)	11.170	2	0.004
catChoiceCondition:scaledValueDiff	0.780	1	0.377

library(kableExtra)
kbl(car::Anova(model.logRT.i,type="3"),digits = 3) %>%
  kable_classic(full_width = F, html_font = "Cambria")

## Warning in printHypothesis(L, rhs, names(b)): one or more coefficients in the hypothesis include
##      arithmetic operators in their names;
##   the printed representation of the hypothesis will be omitted
## Warning in printHypothesis(L, rhs, names(b)): one or more coefficients in the hypothesis include
##      arithmetic operators in their names;
##   the printed representation of the hypothesis will be omitted
## Warning in printHypothesis(L, rhs, names(b)): one or more coefficients in the hypothesis include
##      arithmetic operators in their names;
##   the printed representation of the hypothesis will be omitted

	Chisq	Df	Pr(>Chisq)
(Intercept)	529.317	1	0.000
catChoiceCondition	6.040	1	0.014
scaledMeanValue	30.254	1	0.000
scaledValueDiff	155.705	1	0.000
scaledTrialNum	107.151	1	0.000
catChoiceCondition:scaledMeanValue	4.943	1	0.026
catChoiceCondition:scaledValueDiff	1.353	1	0.245

kbl(car::Anova(model.acc.i,type="3"),digits = 3) %>%
  kable_classic(full_width = F, html_font = "Cambria")

## Warning in printHypothesis(L, rhs, names(b)): one or more coefficients in the hypothesis include
##      arithmetic operators in their names;
##   the printed representation of the hypothesis will be omitted
## Warning in printHypothesis(L, rhs, names(b)): one or more coefficients in the hypothesis include
##      arithmetic operators in their names;
##   the printed representation of the hypothesis will be omitted
## Warning in printHypothesis(L, rhs, names(b)): one or more coefficients in the hypothesis include
##      arithmetic operators in their names;
##   the printed representation of the hypothesis will be omitted

	Chisq	Df	Pr(>Chisq)
(Intercept)	19.270	1	0.000
catChoiceCondition	1.685	1	0.194
scaledMeanValue	1.674	1	0.196
scaledValueDiff	267.755	1	0.000
scaledTrialNum	2.027	1	0.155
catChoiceCondition:scaledMeanValue	0.026	1	0.873
catChoiceCondition:scaledValueDiff	0.357	1	0.550

kbl(car::Anova(model.conflict.i,type="3"),digits = 3) %>%
  kable_classic(full_width = F, html_font = "Cambria")

## Warning in printHypothesis(L, rhs, names(b)): one or more coefficients in the hypothesis include
##      arithmetic operators in their names;
##   the printed representation of the hypothesis will be omitted
## Warning in printHypothesis(L, rhs, names(b)): one or more coefficients in the hypothesis include
##      arithmetic operators in their names;
##   the printed representation of the hypothesis will be omitted
## Warning in printHypothesis(L, rhs, names(b)): one or more coefficients in the hypothesis include
##      arithmetic operators in their names;
##   the printed representation of the hypothesis will be omitted

	Chisq	Df	Pr(>Chisq)
(Intercept)	697.799	1	0.000
catChoiceCondition	6.046	1	0.014
poly(scaledMeanValue, 2)	20.652	2	0.000
scaledValueDiff	9.372	1	0.002
scaledTrialNum	0.374	1	0.541
catChoiceCondition:poly(scaledMeanValue, 2)	5.797	2	0.055
catChoiceCondition:scaledValueDiff	0.070	1	0.791

6 Study 6

df.rating.6 <- read.csv('../Data/Study6/Study6_2.csv')

df.total.cfl.6 <- read.csv('../Data/Study6/Study6_1.csv') %>%
  mutate(catChoiceCondition=factor(choiceCondition,labels = c('OR','XOR'))) %>%
  mutate(isBestFirst=firstValue==bestValue) %>%
  mutate(scaledTrialNum=scale(trialNGlobal),
         scaledVarValue=scale(varValue),
         scaledValueDiff2=scale(bestValue-worstValue),
         scaledMeanValue=scale(meanValue),
         scaledValueDiff=scale(valueDiff))

df.total.rt.cfl.6 <- df.total.cfl.6 %>% filter(firstRT>0.1) %>%
  mutate(scaledTrialNum=scale(trialNGlobal),
         scaledMeanValue=scale(meanValue),
         scaledVarValue=scale(varValue),
         scaledValueDiff=scale(valueDiff),
         scaledRT=scale(firstRT),
         catAcc=factor(isBestFirst))
contrasts(df.total.rt.cfl.6$catAcc)<-contr.sum
df.total.rt.cfl.6$catChoiceCondition<-relevel(df.total.rt.cfl.6$catChoiceCondition,'XOR')
df.total.cfl.6$catChoiceCondition<-relevel(df.total.cfl.6$catChoiceCondition,'XOR')
contrasts(df.total.rt.cfl.6$catChoiceCondition)<-MASS::contr.sdif
contrasts(df.total.cfl.6$catChoiceCondition)<-MASS::contr.sdif

model.FRT.cfl <- lmerTest::lmer(log10(firstRT) ~ catChoiceCondition * (scaledMeanValue + scaledValueDiff) + scaledTrialNum + (1 + catChoiceCondition * (scaledMeanValue + scaledValueDiff) + scaledTrialNum|participant),data=df.total.rt.cfl.6,control=lmerControl(optCtrl=list(maxfun=50000) ))

## boundary (singular) fit: see help('isSingular')

model.acc.cfl <- glmer(isBestFirst ~ catChoiceCondition * scaledMeanValue +  catChoiceCondition * scaledValueDiff + scaledTrialNum + (1 + catChoiceCondition * scaledMeanValue +  catChoiceCondition * scaledValueDiff + scaledTrialNum|participant),data=df.total.rt.cfl.6,family = binomial)

## Warning in (function (fn, par, lower = rep.int(-Inf, n), upper = rep.int(Inf, :
## failure to converge in 10000 evaluations

## Warning in optwrap(optimizer, devfun, start, rho$lower, control = control, :
## convergence code 4 from Nelder_Mead: failure to converge in 10000 evaluations

## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 0.0969178 (tol = 0.002, component 1)

model.rating.cfl <- lmerTest::lmer(conflict ~ catChoiceCondition * (poly(scaledMeanValue,2) + scaledValueDiff) + scaledTrialNum + (1 + catChoiceCondition * (poly(scaledMeanValue,2) + scaledValueDiff) + scaledTrialNum|participant),data=df.total.rt.cfl.6,control=lmerControl(optCtrl=list(maxfun=100000)))

## boundary (singular) fit: see help('isSingular')

## Warning: Model failed to converge with 2 negative eigenvalues: -1.5e-04
## -3.4e-03

coeff.rt.ns <- fixef(model.FRT.cfl)[c('catChoiceConditionOR-XOR','catChoiceConditionOR-XOR:scaledMeanValue','catChoiceConditionOR-XOR:scaledValueDiff')]
df.ci <- confint(model.FRT.cfl,method="Wald")
df.ci <- df.ci[!is.na(df.ci[,1]),]
ci.rt <- df.ci[c('catChoiceConditionOR-XOR','catChoiceConditionOR-XOR:scaledMeanValue','catChoiceConditionOR-XOR:scaledValueDiff'),]
estimate.rt.i <- t(rbind(coeff.rt.ns,t(ci.rt)))
colnames(estimate.rt.i)<-c('coeff','lower','upper')
rownames(estimate.rt.i) <- NULL
estimate.rt.i <- data.frame(estimate.rt.i)
estimate.rt.i$params <- c('Incl - Excl','(Incl - Excl) X OV','(Incl - Excl) X RV')
estimate.rt.i$dv <- 'RT'

p.summary.i.rt <- ggplot(estimate.rt.i,aes(x=params,y=coeff)) + geom_hline(yintercept=0,color='#AAAAAA',size=0.2) + geom_point(position = position_dodge(0.6),size=0.5) + geom_errorbar(position = position_dodge(0.6),aes(ymin=lower,ymax=upper),width=0.2) + coord_flip() + theme_bw(12) + 
  theme(panel.border = element_blank(),panel.grid.major = element_blank(),
        axis.title.x = element_text(margin = margin(t = 0, r = 0, b = 0, l = 0)),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),
        axis.ticks = element_line(colour = "black",size=0.2),
        text=element_text(size=6),legend.position="none") + scale_y_continuous(limits = c(-0.04,0.04),breaks = c(-0.04,0,0.04)) + xlab('') + ylab('') + scale_x_discrete(labels=c('Incl - Excl'='On intercept','(Incl - Excl) X OV'='On overall value effect','(Incl - Excl) X RV'='On relative value effect'))
p.summary.i.rt

ggsave(filename = '../Figures/FigureS2A.pdf',p.summary.i.rt,units = 'cm',width = 4.8,height = 3)

eff_mv.acc.3 <- Effect(c("scaledMeanValue","catChoiceCondition"),
                   model.rating.cfl,
                   xlevels=list(scaledMeanValue=seq(quantile(df.total.rt.cfl.6$scaledMeanValue,0.025),
                                                    quantile(df.total.rt.cfl.6$scaledMeanValue,0.975),0.1)
                                ))

## Warning in Analyze.model(focal.predictors, mod, xlevels, default.levels, : the
## predictors scaledValueDiff, scaledTrialNum, scaledMeanValue are one-column
## matrices that were converted to vectors

IA.mv.acc.3 <- as.data.frame(eff_mv.acc.3) %>% dplyr::mutate(study='Study 3')

p.eff.mv.acc.3 <-ggplot(data=IA.mv.acc.3, aes(x=scaledMeanValue, y=fit, group=catChoiceCondition)) + 
  geom_line(size=0.5,aes(color=catChoiceCondition))+theme_bw(12) +
  geom_ribbon(data=IA.mv.acc.3, aes(x=scaledMeanValue, max = lower, min = upper,fill=catChoiceCondition),alpha=0.3, inherit.aes = FALSE)+ 
  xlab("Overall value\n(z-scored)") + ylab("Conflict") + 
  theme(panel.border = element_blank(), panel.grid.major = element_blank(), 
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),
        axis.ticks = element_line(colour = "black",size=0.2)) +
  theme(text = element_text(size=6),legend.position = 'none') + 
  scale_fill_manual("",values=c('#0673C3','#00B024')) + 
  scale_color_manual("",values=c('#0673C3','#00B024'))

p.eff.mv.acc.3

ggsave(filename = '../Figures/FigureS2B.pdf',p.eff.mv.acc.3,units = 'cm',width = 3,height = 3)

marginalConflictMVEffect <- function(model,x,newx) {
  poly.base <- poly(x,2)
  
  new_poly <- predict(poly.base,newx)
  
  coeffs.mv.1 <- summary(model)$coeff[,'Estimate']
  
  eff <- coeffs.mv.1['catChoiceConditionOR-XOR'] + 
    coeffs.mv.1['catChoiceConditionOR-XOR:poly(scaledMeanValue, 2)1']*new_poly[,1] + 
    coeffs.mv.1['catChoiceConditionOR-XOR:poly(scaledMeanValue, 2)2']*new_poly[,2]
  
  cov.mat <- vcov(model)
  
  eff.ci <- 1.96 * sqrt(cov.mat[2,2] + new_poly[,1]^2 * cov.mat[7,7] + new_poly[,2]^2 * cov.mat[8,8] + 
                                 2 * new_poly[,1] * cov.mat[2,7] + 2 * new_poly[,2] * cov.mat[2,8] + 
                                 2 * new_poly[,1] * new_poly[,2] * cov.mat[7,8])
  
  eff.df<-data.frame(x=newx,eff=eff,ci=eff.ci)
  
  return(eff.df)
}

new.mv.1 <- seq(quantile(df.total.rt.cfl.6$scaledMeanValue,0.025),
                quantile(df.total.rt.cfl.6$scaledMeanValue,0.975),0.1)

eff.df.mv.12 <- marginalConflictMVEffect(model.rating.cfl,
                                         df.total.rt.cfl.6$scaledMeanValue,
                                         new.mv.1) %>%
  dplyr::mutate(scaledMeanValue=x,
                catChoiceCondition='XOR - OR',
                fit=eff,
                upper=eff+ci,
                lower=eff-ci,
                se=NA,
                study='Study 12')

p.eff.cc.int.12<-ggplot(data=eff.df.mv.12, aes(x=x, y=fit)) + 
  geom_line(size=0.5)+theme_bw(12) +
  geom_ribbon(data=eff.df.mv.12, aes(x=x, max = upper, min = lower),alpha=0.3, inherit.aes = FALSE)+ 
  xlab("Overall value\n(z-scored)") + ylab('Effect of Inclusivity') +
  theme(panel.border = element_blank(), panel.grid.major = element_blank(), plot.title = element_text(hjust = 0.5,size=6),
        panel.grid.minor = element_blank(), axis.line = element_line(colour = "black",size=0.2),strip.text.y = element_blank(),
        axis.ticks = element_line(colour = "black",size=0.2)) +
  theme(legend.justification=c(1,1),legend.position='none',text = element_text(size=6)) + geom_hline(yintercept=0,color='#555555',size=0.2) + #ggtitle('Conflict') +
  coord_cartesian(ylim=c(-1,0.1)) + scale_y_continuous(breaks = c(-1,0))

p.eff.cc.int.12

ggsave(filename = '../Figures/FigureS2C.pdf',p.eff.cc.int.12,units = 'cm',width = 3,height = 3)